SlideShare a Scribd company logo
TUGAS
MATEMATIKA
DISKRIT
KELOMPOK 5
Nama Anggota :
1. Annisa Raudatul Jannah (E1R014006)
2. Arli Sarosa (E1R014008)
3. Fitri Handayani (E1R014017)
4. Robi Indrawan (E1R014048)
Kelas A Matematika Pagi Semester 5
FAKULTAS KEGURUAN DAN ILMU PENDIDIKAN
UNIVERSITAS MATARAM
2016
AKAR KOMPELKS (Z)
(cos + i sin )n
= cos n + i sin n , n 0
Sebelum membahas tentang akar kompleks, kita bahas terlebih dahulu Teorema De Moivre’s,
yaitu:
Jika ,
kita bisa menuliskan
dan
Dari persamaan di atas, kita dapat menggambarkan secara kartesius maupun polar
cos = r cos = x
sin = r sin = y Substitusi ke z = x + yi
tan = x tan = y
Z = x + yi
= r cos + (r sin ) i
= r (cos + i sin )
= r (cis )
Z1 = r1 (cos 1 + i sin 1)
Z2 = r2 (cos 2 + i sin 2)
Z1 . Z2 = r1 . r2 (cos 1 + i sin 1) (cos 2 + i sin 2)
= r1 . r2 [ cos (1+ 2) + i sin (1 + 2)
Z1 . Z2 . .... . Zn = r1 . r2 . .... . rn cis ( 1 + 2 + ... + n )
 Jika Z1 = Z2 = ... = Zn = Z, maka kita dapat menemukan dalil de Moivre
Z
n
= r
n
cis (n)
 CONTOH 1
Tentukan Z
10
, dimana Z = (1 + i)
(x,y) = (1 + )
Penyelesaian:
r =
=
=
= 2
tan =
=
=
= 60o
=
Z
n
= r
n
cis (n)
Z
10
= r
10
cis (10 .)
= 210
[ cos () + i sin ()]
= 210
[ (−) + i ()]
= 210
[− i]
= 210
(−) [1 + i ]
= 29
[1 + i ]
= 29
+ (29
) i
C0an + C1 an-1 + C2an-2 + ... + Ckan-k = f (n), n k
an + an-1 - 6 an-2 = 0, n 2 a0 = -1 a1 = 8
an = crn
, c, r 0
crn
+ crn-1
- 6 crn-2
= 0
r2
+ r – 6 = 0
(r +3)(r - 2) = 0
r = -3 V r = 2
 CONTOH 2
an=2(an-1 – an-2), n ≥ 2, ao = 1, a1 = 2
r2
– 2r + 2
Penyelesaian:
Dengan memakai rumus abc, didapatkan:
an = c1 . r1
n
+ c2r2
n
= c1 (1 + I) + c2 (1 – i)
z = x + iy
Sehingga,
ao = 1, a2 = 2
1 = ao = (k1 cos () + k2 sin ())
1 = k1
2 = a1 = (k1 cos () + k2 sin ())
2 = 1 + k2
2 – 1 = k2
1 = k2
ao = 1, a2 = 2
1 = ao = (k1 cos () + k2 sin ())
1 = k1
2 = a1 = (k1 cos () + k2 sin ())
2 = 1 + k2
2 – 1 = k2
1 = k2

More Related Content

What's hot

2.7 more parabolas a& hyperbolas (optional) t
2.7 more parabolas a& hyperbolas (optional) t2.7 more parabolas a& hyperbolas (optional) t
2.7 more parabolas a& hyperbolas (optional) t
math260
 
Complexos 3
Complexos 3Complexos 3
Complexos 3
KalculosOnline
 
Binômio de Newton 2
Binômio de Newton 2Binômio de Newton 2
Binômio de Newton 2
KalculosOnline
 
Test yourself for JEE(Main)TP-5
Test yourself for JEE(Main)TP-5Test yourself for JEE(Main)TP-5
Test yourself for JEE(Main)TP-5
Vijay Joglekar
 
Álgebra básica 2
Álgebra básica 2Álgebra básica 2
Álgebra básica 2
KalculosOnline
 
Test yourself for JEE(Main)TP-4
Test yourself for JEE(Main)TP-4Test yourself for JEE(Main)TP-4
Test yourself for JEE(Main)TP-4
Vijay Joglekar
 
Fuvest 2019 - aberta
Fuvest 2019 - abertaFuvest 2019 - aberta
Fuvest 2019 - aberta
KalculosOnline
 
Math graphing quatratic equation
Math graphing quatratic equationMath graphing quatratic equation
Math graphing quatratic equation
student
 
Đề Thi HK2 Toán 9 - TH THCS THPT  Mỹ Việt
Đề Thi HK2 Toán 9 - TH THCS THPT  Mỹ ViệtĐề Thi HK2 Toán 9 - TH THCS THPT  Mỹ Việt
Đề Thi HK2 Toán 9 - TH THCS THPT  Mỹ Việt
Trung Tâm Gia Sư Việt Trí
 
Trigonometry
TrigonometryTrigonometry
Trigonometry
Vijay Joglekar
 
Đề Thi HK2 Toán 6 - THCS Nguyễn Minh Hoàng
Đề Thi HK2 Toán 6 - THCS Nguyễn Minh HoàngĐề Thi HK2 Toán 6 - THCS Nguyễn Minh Hoàng
Đề Thi HK2 Toán 6 - THCS Nguyễn Minh Hoàng
Trung Tâm Gia Sư Việt Trí
 
Magical Short Tricks for JEE(Main).
Magical Short Tricks for JEE(Main).Magical Short Tricks for JEE(Main).
Magical Short Tricks for JEE(Main).
Vijay Joglekar
 
ITA 2012 - fechada
ITA 2012 - fechadaITA 2012 - fechada
ITA 2012 - fechada
KalculosOnline
 
Đề Thi HK2 Toán 9 - TH THCS THPT  Emasi Nam Long
Đề Thi HK2 Toán 9 - TH THCS THPT  Emasi Nam LongĐề Thi HK2 Toán 9 - TH THCS THPT  Emasi Nam Long
Đề Thi HK2 Toán 9 - TH THCS THPT  Emasi Nam Long
Trung Tâm Gia Sư Việt Trí
 
Conceptual Short Tricks for JEE(Main and Advanced)
Conceptual Short Tricks for JEE(Main and Advanced)Conceptual Short Tricks for JEE(Main and Advanced)
Conceptual Short Tricks for JEE(Main and Advanced)
Pony Joglekar
 
8th PreAlg - L73--April2
8th PreAlg - L73--April28th PreAlg - L73--April2
8th PreAlg - L73--April2jdurst65
 

What's hot (19)

2.7 more parabolas a& hyperbolas (optional) t
2.7 more parabolas a& hyperbolas (optional) t2.7 more parabolas a& hyperbolas (optional) t
2.7 more parabolas a& hyperbolas (optional) t
 
Ecat math
Ecat mathEcat math
Ecat math
 
Complexos 3
Complexos 3Complexos 3
Complexos 3
 
Binômio de Newton 2
Binômio de Newton 2Binômio de Newton 2
Binômio de Newton 2
 
Test yourself for JEE(Main)TP-5
Test yourself for JEE(Main)TP-5Test yourself for JEE(Main)TP-5
Test yourself for JEE(Main)TP-5
 
Álgebra básica 2
Álgebra básica 2Álgebra básica 2
Álgebra básica 2
 
Test yourself for JEE(Main)TP-4
Test yourself for JEE(Main)TP-4Test yourself for JEE(Main)TP-4
Test yourself for JEE(Main)TP-4
 
Fuvest 2019 - aberta
Fuvest 2019 - abertaFuvest 2019 - aberta
Fuvest 2019 - aberta
 
Math graphing quatratic equation
Math graphing quatratic equationMath graphing quatratic equation
Math graphing quatratic equation
 
Đề Thi HK2 Toán 9 - TH THCS THPT  Mỹ Việt
Đề Thi HK2 Toán 9 - TH THCS THPT  Mỹ ViệtĐề Thi HK2 Toán 9 - TH THCS THPT  Mỹ Việt
Đề Thi HK2 Toán 9 - TH THCS THPT  Mỹ Việt
 
Trigonometry
TrigonometryTrigonometry
Trigonometry
 
Đề Thi HK2 Toán 6 - THCS Nguyễn Minh Hoàng
Đề Thi HK2 Toán 6 - THCS Nguyễn Minh HoàngĐề Thi HK2 Toán 6 - THCS Nguyễn Minh Hoàng
Đề Thi HK2 Toán 6 - THCS Nguyễn Minh Hoàng
 
Magical Short Tricks for JEE(Main).
Magical Short Tricks for JEE(Main).Magical Short Tricks for JEE(Main).
Magical Short Tricks for JEE(Main).
 
Integral
IntegralIntegral
Integral
 
ITA 2012 - fechada
ITA 2012 - fechadaITA 2012 - fechada
ITA 2012 - fechada
 
Đề Thi HK2 Toán 9 - TH THCS THPT  Emasi Nam Long
Đề Thi HK2 Toán 9 - TH THCS THPT  Emasi Nam LongĐề Thi HK2 Toán 9 - TH THCS THPT  Emasi Nam Long
Đề Thi HK2 Toán 9 - TH THCS THPT  Emasi Nam Long
 
Regras diferenciacao
Regras diferenciacaoRegras diferenciacao
Regras diferenciacao
 
Conceptual Short Tricks for JEE(Main and Advanced)
Conceptual Short Tricks for JEE(Main and Advanced)Conceptual Short Tricks for JEE(Main and Advanced)
Conceptual Short Tricks for JEE(Main and Advanced)
 
8th PreAlg - L73--April2
8th PreAlg - L73--April28th PreAlg - L73--April2
8th PreAlg - L73--April2
 

Similar to 5 matdis akar_kompleks k

IIT Jam math 2016 solutions BY Trajectoryeducation
IIT Jam math 2016 solutions BY TrajectoryeducationIIT Jam math 2016 solutions BY Trajectoryeducation
IIT Jam math 2016 solutions BY Trajectoryeducation
Dev Singh
 
2 complex numbers part 2 of 3
2 complex numbers part 2 of 32 complex numbers part 2 of 3
2 complex numbers part 2 of 3
naveenkumar9211
 
ArithmeticProgression
ArithmeticProgression ArithmeticProgression
ArithmeticProgression
Prashant Jain
 
cl 9 polynomial.pdf
cl 9 polynomial.pdfcl 9 polynomial.pdf
cl 9 polynomial.pdf
TanishqAgarwal27
 
Class 11 Cbse Maths Sample Paper 2012
Class 11 Cbse Maths Sample Paper 2012Class 11 Cbse Maths Sample Paper 2012
Class 11 Cbse Maths Sample Paper 2012
Sunaina Rawat
 
maths ppt.pdf
maths ppt.pdfmaths ppt.pdf
maths ppt.pdf
nihaiqbal1
 
maths ppt.pdf
maths ppt.pdfmaths ppt.pdf
maths ppt.pdf
nihaiqbal1
 
Trigonometry - Formula Sheet - MathonGo.pdf
Trigonometry - Formula Sheet - MathonGo.pdfTrigonometry - Formula Sheet - MathonGo.pdf
Trigonometry - Formula Sheet - MathonGo.pdf
Elango Palaniappan
 
Aieee maths-quick review
Aieee maths-quick reviewAieee maths-quick review
Aieee maths-quick reviewSharath Kumar
 
Shahjahan notes:Mathematicsinphysicstheorysampleproblematc
Shahjahan notes:MathematicsinphysicstheorysampleproblematcShahjahan notes:Mathematicsinphysicstheorysampleproblematc
Shahjahan notes:Mathematicsinphysicstheorysampleproblematc
Shahjahan Physics
 
1st semester chemistry stream (2015-June) Question Papers
1st semester chemistry stream (2015-June) Question Papers 1st semester chemistry stream (2015-June) Question Papers
1st semester chemistry stream (2015-June) Question Papers
BGS Institute of Technology, Adichunchanagiri University (ACU)
 
A Solutions To Exercises On Complex Numbers
A Solutions To Exercises On Complex NumbersA Solutions To Exercises On Complex Numbers
A Solutions To Exercises On Complex Numbers
Scott Bou
 
MATHEMATICS XI TEST PAPER SOL.pdf
MATHEMATICS XI TEST PAPER SOL.pdfMATHEMATICS XI TEST PAPER SOL.pdf
MATHEMATICS XI TEST PAPER SOL.pdf
Ashwani Jha
 
CIRCLES.pptx
CIRCLES.pptxCIRCLES.pptx
CIRCLES.pptx
vannessafaithgobot
 
Presentation on calculus
Presentation on calculusPresentation on calculus
Presentation on calculus
Shariful Haque Robin
 
Circunfêrencia 2
Circunfêrencia 2Circunfêrencia 2
Circunfêrencia 2
KalculosOnline
 
Add math may june 2016 p1
Add math may june 2016 p1Add math may june 2016 p1
Add math may june 2016 p1
Don Cunningham
 
mathematics part-2.docx
mathematics part-2.docxmathematics part-2.docx
mathematics part-2.docx
Lakeshkumarpadhy
 
Succesive differntiation
Succesive differntiationSuccesive differntiation
Succesive differntiation
JaydevVadachhak
 
(Www.entrance exam.net)-sail placement sample paper 5
(Www.entrance exam.net)-sail placement sample paper 5(Www.entrance exam.net)-sail placement sample paper 5
(Www.entrance exam.net)-sail placement sample paper 5SAMEER NAIK
 

Similar to 5 matdis akar_kompleks k (20)

IIT Jam math 2016 solutions BY Trajectoryeducation
IIT Jam math 2016 solutions BY TrajectoryeducationIIT Jam math 2016 solutions BY Trajectoryeducation
IIT Jam math 2016 solutions BY Trajectoryeducation
 
2 complex numbers part 2 of 3
2 complex numbers part 2 of 32 complex numbers part 2 of 3
2 complex numbers part 2 of 3
 
ArithmeticProgression
ArithmeticProgression ArithmeticProgression
ArithmeticProgression
 
cl 9 polynomial.pdf
cl 9 polynomial.pdfcl 9 polynomial.pdf
cl 9 polynomial.pdf
 
Class 11 Cbse Maths Sample Paper 2012
Class 11 Cbse Maths Sample Paper 2012Class 11 Cbse Maths Sample Paper 2012
Class 11 Cbse Maths Sample Paper 2012
 
maths ppt.pdf
maths ppt.pdfmaths ppt.pdf
maths ppt.pdf
 
maths ppt.pdf
maths ppt.pdfmaths ppt.pdf
maths ppt.pdf
 
Trigonometry - Formula Sheet - MathonGo.pdf
Trigonometry - Formula Sheet - MathonGo.pdfTrigonometry - Formula Sheet - MathonGo.pdf
Trigonometry - Formula Sheet - MathonGo.pdf
 
Aieee maths-quick review
Aieee maths-quick reviewAieee maths-quick review
Aieee maths-quick review
 
Shahjahan notes:Mathematicsinphysicstheorysampleproblematc
Shahjahan notes:MathematicsinphysicstheorysampleproblematcShahjahan notes:Mathematicsinphysicstheorysampleproblematc
Shahjahan notes:Mathematicsinphysicstheorysampleproblematc
 
1st semester chemistry stream (2015-June) Question Papers
1st semester chemistry stream (2015-June) Question Papers 1st semester chemistry stream (2015-June) Question Papers
1st semester chemistry stream (2015-June) Question Papers
 
A Solutions To Exercises On Complex Numbers
A Solutions To Exercises On Complex NumbersA Solutions To Exercises On Complex Numbers
A Solutions To Exercises On Complex Numbers
 
MATHEMATICS XI TEST PAPER SOL.pdf
MATHEMATICS XI TEST PAPER SOL.pdfMATHEMATICS XI TEST PAPER SOL.pdf
MATHEMATICS XI TEST PAPER SOL.pdf
 
CIRCLES.pptx
CIRCLES.pptxCIRCLES.pptx
CIRCLES.pptx
 
Presentation on calculus
Presentation on calculusPresentation on calculus
Presentation on calculus
 
Circunfêrencia 2
Circunfêrencia 2Circunfêrencia 2
Circunfêrencia 2
 
Add math may june 2016 p1
Add math may june 2016 p1Add math may june 2016 p1
Add math may june 2016 p1
 
mathematics part-2.docx
mathematics part-2.docxmathematics part-2.docx
mathematics part-2.docx
 
Succesive differntiation
Succesive differntiationSuccesive differntiation
Succesive differntiation
 
(Www.entrance exam.net)-sail placement sample paper 5
(Www.entrance exam.net)-sail placement sample paper 5(Www.entrance exam.net)-sail placement sample paper 5
(Www.entrance exam.net)-sail placement sample paper 5
 

Recently uploaded

Chapter 3 - Islamic Banking Products and Services.pptx
Chapter 3 - Islamic Banking Products and Services.pptxChapter 3 - Islamic Banking Products and Services.pptx
Chapter 3 - Islamic Banking Products and Services.pptx
Mohd Adib Abd Muin, Senior Lecturer at Universiti Utara Malaysia
 
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...
Levi Shapiro
 
Guidance_and_Counselling.pdf B.Ed. 4th Semester
Guidance_and_Counselling.pdf B.Ed. 4th SemesterGuidance_and_Counselling.pdf B.Ed. 4th Semester
Guidance_and_Counselling.pdf B.Ed. 4th Semester
Atul Kumar Singh
 
1.4 modern child centered education - mahatma gandhi-2.pptx
1.4 modern child centered education - mahatma gandhi-2.pptx1.4 modern child centered education - mahatma gandhi-2.pptx
1.4 modern child centered education - mahatma gandhi-2.pptx
JosvitaDsouza2
 
Unit 8 - Information and Communication Technology (Paper I).pdf
Unit 8 - Information and Communication Technology (Paper I).pdfUnit 8 - Information and Communication Technology (Paper I).pdf
Unit 8 - Information and Communication Technology (Paper I).pdf
Thiyagu K
 
The Challenger.pdf DNHS Official Publication
The Challenger.pdf DNHS Official PublicationThe Challenger.pdf DNHS Official Publication
The Challenger.pdf DNHS Official Publication
Delapenabediema
 
special B.ed 2nd year old paper_20240531.pdf
special B.ed 2nd year old paper_20240531.pdfspecial B.ed 2nd year old paper_20240531.pdf
special B.ed 2nd year old paper_20240531.pdf
Special education needs
 
A Strategic Approach: GenAI in Education
A Strategic Approach: GenAI in EducationA Strategic Approach: GenAI in Education
A Strategic Approach: GenAI in Education
Peter Windle
 
Home assignment II on Spectroscopy 2024 Answers.pdf
Home assignment II on Spectroscopy 2024 Answers.pdfHome assignment II on Spectroscopy 2024 Answers.pdf
Home assignment II on Spectroscopy 2024 Answers.pdf
Tamralipta Mahavidyalaya
 
Model Attribute Check Company Auto Property
Model Attribute  Check Company Auto PropertyModel Attribute  Check Company Auto Property
Model Attribute Check Company Auto Property
Celine George
 
Mule 4.6 & Java 17 Upgrade | MuleSoft Mysore Meetup #46
Mule 4.6 & Java 17 Upgrade | MuleSoft Mysore Meetup #46Mule 4.6 & Java 17 Upgrade | MuleSoft Mysore Meetup #46
Mule 4.6 & Java 17 Upgrade | MuleSoft Mysore Meetup #46
MysoreMuleSoftMeetup
 
Synthetic Fiber Construction in lab .pptx
Synthetic Fiber Construction in lab .pptxSynthetic Fiber Construction in lab .pptx
Synthetic Fiber Construction in lab .pptx
Pavel ( NSTU)
 
Language Across the Curriculm LAC B.Ed.
Language Across the  Curriculm LAC B.Ed.Language Across the  Curriculm LAC B.Ed.
Language Across the Curriculm LAC B.Ed.
Atul Kumar Singh
 
Honest Reviews of Tim Han LMA Course Program.pptx
Honest Reviews of Tim Han LMA Course Program.pptxHonest Reviews of Tim Han LMA Course Program.pptx
Honest Reviews of Tim Han LMA Course Program.pptx
timhan337
 
The Roman Empire A Historical Colossus.pdf
The Roman Empire A Historical Colossus.pdfThe Roman Empire A Historical Colossus.pdf
The Roman Empire A Historical Colossus.pdf
kaushalkr1407
 
Lapbook sobre os Regimes Totalitários.pdf
Lapbook sobre os Regimes Totalitários.pdfLapbook sobre os Regimes Totalitários.pdf
Lapbook sobre os Regimes Totalitários.pdf
Jean Carlos Nunes Paixão
 
Biological Screening of Herbal Drugs in detailed.
Biological Screening of Herbal Drugs in detailed.Biological Screening of Herbal Drugs in detailed.
Biological Screening of Herbal Drugs in detailed.
Ashokrao Mane college of Pharmacy Peth-Vadgaon
 
The approach at University of Liverpool.pptx
The approach at University of Liverpool.pptxThe approach at University of Liverpool.pptx
The approach at University of Liverpool.pptx
Jisc
 
Thesis Statement for students diagnonsed withADHD.ppt
Thesis Statement for students diagnonsed withADHD.pptThesis Statement for students diagnonsed withADHD.ppt
Thesis Statement for students diagnonsed withADHD.ppt
EverAndrsGuerraGuerr
 
How libraries can support authors with open access requirements for UKRI fund...
How libraries can support authors with open access requirements for UKRI fund...How libraries can support authors with open access requirements for UKRI fund...
How libraries can support authors with open access requirements for UKRI fund...
Jisc
 

Recently uploaded (20)

Chapter 3 - Islamic Banking Products and Services.pptx
Chapter 3 - Islamic Banking Products and Services.pptxChapter 3 - Islamic Banking Products and Services.pptx
Chapter 3 - Islamic Banking Products and Services.pptx
 
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...
 
Guidance_and_Counselling.pdf B.Ed. 4th Semester
Guidance_and_Counselling.pdf B.Ed. 4th SemesterGuidance_and_Counselling.pdf B.Ed. 4th Semester
Guidance_and_Counselling.pdf B.Ed. 4th Semester
 
1.4 modern child centered education - mahatma gandhi-2.pptx
1.4 modern child centered education - mahatma gandhi-2.pptx1.4 modern child centered education - mahatma gandhi-2.pptx
1.4 modern child centered education - mahatma gandhi-2.pptx
 
Unit 8 - Information and Communication Technology (Paper I).pdf
Unit 8 - Information and Communication Technology (Paper I).pdfUnit 8 - Information and Communication Technology (Paper I).pdf
Unit 8 - Information and Communication Technology (Paper I).pdf
 
The Challenger.pdf DNHS Official Publication
The Challenger.pdf DNHS Official PublicationThe Challenger.pdf DNHS Official Publication
The Challenger.pdf DNHS Official Publication
 
special B.ed 2nd year old paper_20240531.pdf
special B.ed 2nd year old paper_20240531.pdfspecial B.ed 2nd year old paper_20240531.pdf
special B.ed 2nd year old paper_20240531.pdf
 
A Strategic Approach: GenAI in Education
A Strategic Approach: GenAI in EducationA Strategic Approach: GenAI in Education
A Strategic Approach: GenAI in Education
 
Home assignment II on Spectroscopy 2024 Answers.pdf
Home assignment II on Spectroscopy 2024 Answers.pdfHome assignment II on Spectroscopy 2024 Answers.pdf
Home assignment II on Spectroscopy 2024 Answers.pdf
 
Model Attribute Check Company Auto Property
Model Attribute  Check Company Auto PropertyModel Attribute  Check Company Auto Property
Model Attribute Check Company Auto Property
 
Mule 4.6 & Java 17 Upgrade | MuleSoft Mysore Meetup #46
Mule 4.6 & Java 17 Upgrade | MuleSoft Mysore Meetup #46Mule 4.6 & Java 17 Upgrade | MuleSoft Mysore Meetup #46
Mule 4.6 & Java 17 Upgrade | MuleSoft Mysore Meetup #46
 
Synthetic Fiber Construction in lab .pptx
Synthetic Fiber Construction in lab .pptxSynthetic Fiber Construction in lab .pptx
Synthetic Fiber Construction in lab .pptx
 
Language Across the Curriculm LAC B.Ed.
Language Across the  Curriculm LAC B.Ed.Language Across the  Curriculm LAC B.Ed.
Language Across the Curriculm LAC B.Ed.
 
Honest Reviews of Tim Han LMA Course Program.pptx
Honest Reviews of Tim Han LMA Course Program.pptxHonest Reviews of Tim Han LMA Course Program.pptx
Honest Reviews of Tim Han LMA Course Program.pptx
 
The Roman Empire A Historical Colossus.pdf
The Roman Empire A Historical Colossus.pdfThe Roman Empire A Historical Colossus.pdf
The Roman Empire A Historical Colossus.pdf
 
Lapbook sobre os Regimes Totalitários.pdf
Lapbook sobre os Regimes Totalitários.pdfLapbook sobre os Regimes Totalitários.pdf
Lapbook sobre os Regimes Totalitários.pdf
 
Biological Screening of Herbal Drugs in detailed.
Biological Screening of Herbal Drugs in detailed.Biological Screening of Herbal Drugs in detailed.
Biological Screening of Herbal Drugs in detailed.
 
The approach at University of Liverpool.pptx
The approach at University of Liverpool.pptxThe approach at University of Liverpool.pptx
The approach at University of Liverpool.pptx
 
Thesis Statement for students diagnonsed withADHD.ppt
Thesis Statement for students diagnonsed withADHD.pptThesis Statement for students diagnonsed withADHD.ppt
Thesis Statement for students diagnonsed withADHD.ppt
 
How libraries can support authors with open access requirements for UKRI fund...
How libraries can support authors with open access requirements for UKRI fund...How libraries can support authors with open access requirements for UKRI fund...
How libraries can support authors with open access requirements for UKRI fund...
 

5 matdis akar_kompleks k

  • 1. TUGAS MATEMATIKA DISKRIT KELOMPOK 5 Nama Anggota : 1. Annisa Raudatul Jannah (E1R014006) 2. Arli Sarosa (E1R014008) 3. Fitri Handayani (E1R014017) 4. Robi Indrawan (E1R014048) Kelas A Matematika Pagi Semester 5
  • 2. FAKULTAS KEGURUAN DAN ILMU PENDIDIKAN UNIVERSITAS MATARAM 2016 AKAR KOMPELKS (Z) (cos + i sin )n = cos n + i sin n , n 0 Sebelum membahas tentang akar kompleks, kita bahas terlebih dahulu Teorema De Moivre’s, yaitu: Jika , kita bisa menuliskan dan Dari persamaan di atas, kita dapat menggambarkan secara kartesius maupun polar cos = r cos = x sin = r sin = y Substitusi ke z = x + yi tan = x tan = y Z = x + yi = r cos + (r sin ) i = r (cos + i sin ) = r (cis ) Z1 = r1 (cos 1 + i sin 1) Z2 = r2 (cos 2 + i sin 2) Z1 . Z2 = r1 . r2 (cos 1 + i sin 1) (cos 2 + i sin 2) = r1 . r2 [ cos (1+ 2) + i sin (1 + 2) Z1 . Z2 . .... . Zn = r1 . r2 . .... . rn cis ( 1 + 2 + ... + n )  Jika Z1 = Z2 = ... = Zn = Z, maka kita dapat menemukan dalil de Moivre
  • 3. Z n = r n cis (n)  CONTOH 1 Tentukan Z 10 , dimana Z = (1 + i) (x,y) = (1 + ) Penyelesaian: r = = = = 2 tan = = = = 60o = Z n = r n cis (n) Z 10 = r 10 cis (10 .) = 210 [ cos () + i sin ()]
  • 4. = 210 [ (−) + i ()] = 210 [− i] = 210 (−) [1 + i ] = 29 [1 + i ] = 29 + (29 ) i C0an + C1 an-1 + C2an-2 + ... + Ckan-k = f (n), n k an + an-1 - 6 an-2 = 0, n 2 a0 = -1 a1 = 8 an = crn , c, r 0 crn + crn-1 - 6 crn-2 = 0 r2 + r – 6 = 0 (r +3)(r - 2) = 0 r = -3 V r = 2
  • 5.  CONTOH 2 an=2(an-1 – an-2), n ≥ 2, ao = 1, a1 = 2 r2 – 2r + 2 Penyelesaian: Dengan memakai rumus abc, didapatkan: an = c1 . r1 n + c2r2 n = c1 (1 + I) + c2 (1 – i) z = x + iy Sehingga,
  • 6. ao = 1, a2 = 2 1 = ao = (k1 cos () + k2 sin ()) 1 = k1 2 = a1 = (k1 cos () + k2 sin ()) 2 = 1 + k2 2 – 1 = k2 1 = k2
  • 7. ao = 1, a2 = 2 1 = ao = (k1 cos () + k2 sin ()) 1 = k1 2 = a1 = (k1 cos () + k2 sin ()) 2 = 1 + k2 2 – 1 = k2 1 = k2