SlideShare a Scribd company logo
Use De Moivre's theorem to change the given complex number to the form a + bi, where a and
b are real numbers. (- Squareroot 3/2 - 1/2 i)^4
Solution
( -sqrt3/2 -i/2)^4
Polar form = r*e^i*theta
r = sqrt[ (-sqrt3/2)^2 + (1/2)^2 )] = 1
theta = tan^-1(-1/2 /-sqrt3/2) = pi +pi/3 = 4pi/3
( -sqrt3/2 -i/2)^4 = (re^i*theta)^4 = r^4e^i*4theta
= 1*e^i*16pi/3
= cos16pi/3 + isin16pi/3
= -0.5 -i*0.866

More Related Content

More from arrowvisionoptics

What are the fuctional need of a roadWhat is road building system.pdf
What are the fuctional need of a roadWhat is road building system.pdfWhat are the fuctional need of a roadWhat is road building system.pdf
What are the fuctional need of a roadWhat is road building system.pdf
arrowvisionoptics
 
Why does Germany have to be assertive in the EUSolutionAnswer.pdf
Why does Germany have to be assertive in the EUSolutionAnswer.pdfWhy does Germany have to be assertive in the EUSolutionAnswer.pdf
Why does Germany have to be assertive in the EUSolutionAnswer.pdf
arrowvisionoptics
 
What is the link between wealth and welfare Do governments have a r.pdf
What is the link between wealth and welfare Do governments have a r.pdfWhat is the link between wealth and welfare Do governments have a r.pdf
What is the link between wealth and welfare Do governments have a r.pdf
arrowvisionoptics
 
Which of the following are ways nutrients can enter the root cells .pdf
Which of the following are ways nutrients can enter the root cells  .pdfWhich of the following are ways nutrients can enter the root cells  .pdf
Which of the following are ways nutrients can enter the root cells .pdf
arrowvisionoptics
 
What is E coliSolutionE.coli is a bacteria that normally live.pdf
What is E coliSolutionE.coli is a bacteria that normally live.pdfWhat is E coliSolutionE.coli is a bacteria that normally live.pdf
What is E coliSolutionE.coli is a bacteria that normally live.pdf
arrowvisionoptics
 
Where does mitosis occur in the bodies of vascular plantsSoluti.pdf
Where does mitosis occur in the bodies of vascular plantsSoluti.pdfWhere does mitosis occur in the bodies of vascular plantsSoluti.pdf
Where does mitosis occur in the bodies of vascular plantsSoluti.pdf
arrowvisionoptics
 
Which of the following are the three properties of dataA. mean, m.pdf
Which of the following are the three properties of dataA. mean, m.pdfWhich of the following are the three properties of dataA. mean, m.pdf
Which of the following are the three properties of dataA. mean, m.pdf
arrowvisionoptics
 
What is the range of clinical signssymptoms of C. difficile infecti.pdf
What is the range of clinical signssymptoms of C. difficile infecti.pdfWhat is the range of clinical signssymptoms of C. difficile infecti.pdf
What is the range of clinical signssymptoms of C. difficile infecti.pdf
arrowvisionoptics
 
What was Kants ideas regarding retributive punishmentSolution.pdf
What was Kants ideas regarding retributive punishmentSolution.pdfWhat was Kants ideas regarding retributive punishmentSolution.pdf
What was Kants ideas regarding retributive punishmentSolution.pdf
arrowvisionoptics
 
What are the major events that occur during each stage in the life cy.pdf
What are the major events that occur during each stage in the life cy.pdfWhat are the major events that occur during each stage in the life cy.pdf
What are the major events that occur during each stage in the life cy.pdf
arrowvisionoptics
 
What challenges do corporations face with regards to social media.pdf
What challenges do corporations face with regards to social media.pdfWhat challenges do corporations face with regards to social media.pdf
What challenges do corporations face with regards to social media.pdf
arrowvisionoptics
 
There are no organs for excretion and gas exchange in cnidarians. How.pdf
There are no organs for excretion and gas exchange in cnidarians. How.pdfThere are no organs for excretion and gas exchange in cnidarians. How.pdf
There are no organs for excretion and gas exchange in cnidarians. How.pdf
arrowvisionoptics
 
the term with the definition. Duality Of Effects Journal Entry An amo.pdf
the term with the definition. Duality Of Effects Journal Entry An amo.pdfthe term with the definition. Duality Of Effects Journal Entry An amo.pdf
the term with the definition. Duality Of Effects Journal Entry An amo.pdf
arrowvisionoptics
 
Two proteins are normally found in the cytosol. They are involved in .pdf
Two proteins are normally found in the cytosol. They are involved in .pdfTwo proteins are normally found in the cytosol. They are involved in .pdf
Two proteins are normally found in the cytosol. They are involved in .pdf
arrowvisionoptics
 
Two components operate in parallel in a device, so the device fails .pdf
Two components operate in parallel in a device, so the device fails .pdfTwo components operate in parallel in a device, so the device fails .pdf
Two components operate in parallel in a device, so the device fails .pdf
arrowvisionoptics
 
That assignment had 2 part. I already complated part 1. and collecte.pdf
That assignment had 2 part. I already complated part 1. and collecte.pdfThat assignment had 2 part. I already complated part 1. and collecte.pdf
That assignment had 2 part. I already complated part 1. and collecte.pdf
arrowvisionoptics
 
Book Fundamental of Biostatistics 7th editionProblem pg. 67 #3.1.pdf
Book Fundamental of Biostatistics 7th editionProblem pg. 67 #3.1.pdfBook Fundamental of Biostatistics 7th editionProblem pg. 67 #3.1.pdf
Book Fundamental of Biostatistics 7th editionProblem pg. 67 #3.1.pdf
arrowvisionoptics
 
Stre cell Tran and Homeostasis 5. special proteins in the membrane th.pdf
Stre cell Tran and Homeostasis 5. special proteins in the membrane th.pdfStre cell Tran and Homeostasis 5. special proteins in the membrane th.pdf
Stre cell Tran and Homeostasis 5. special proteins in the membrane th.pdf
arrowvisionoptics
 
Let X and Y be two continuous random variables with probability dens.pdf
Let X and Y be two continuous random variables with probability dens.pdfLet X and Y be two continuous random variables with probability dens.pdf
Let X and Y be two continuous random variables with probability dens.pdf
arrowvisionoptics
 
Many areas of the country have reservoirs or waterways with locks an.pdf
Many areas of the country have reservoirs or waterways with locks an.pdfMany areas of the country have reservoirs or waterways with locks an.pdf
Many areas of the country have reservoirs or waterways with locks an.pdf
arrowvisionoptics
 

More from arrowvisionoptics (20)

What are the fuctional need of a roadWhat is road building system.pdf
What are the fuctional need of a roadWhat is road building system.pdfWhat are the fuctional need of a roadWhat is road building system.pdf
What are the fuctional need of a roadWhat is road building system.pdf
 
Why does Germany have to be assertive in the EUSolutionAnswer.pdf
Why does Germany have to be assertive in the EUSolutionAnswer.pdfWhy does Germany have to be assertive in the EUSolutionAnswer.pdf
Why does Germany have to be assertive in the EUSolutionAnswer.pdf
 
What is the link between wealth and welfare Do governments have a r.pdf
What is the link between wealth and welfare Do governments have a r.pdfWhat is the link between wealth and welfare Do governments have a r.pdf
What is the link between wealth and welfare Do governments have a r.pdf
 
Which of the following are ways nutrients can enter the root cells .pdf
Which of the following are ways nutrients can enter the root cells  .pdfWhich of the following are ways nutrients can enter the root cells  .pdf
Which of the following are ways nutrients can enter the root cells .pdf
 
What is E coliSolutionE.coli is a bacteria that normally live.pdf
What is E coliSolutionE.coli is a bacteria that normally live.pdfWhat is E coliSolutionE.coli is a bacteria that normally live.pdf
What is E coliSolutionE.coli is a bacteria that normally live.pdf
 
Where does mitosis occur in the bodies of vascular plantsSoluti.pdf
Where does mitosis occur in the bodies of vascular plantsSoluti.pdfWhere does mitosis occur in the bodies of vascular plantsSoluti.pdf
Where does mitosis occur in the bodies of vascular plantsSoluti.pdf
 
Which of the following are the three properties of dataA. mean, m.pdf
Which of the following are the three properties of dataA. mean, m.pdfWhich of the following are the three properties of dataA. mean, m.pdf
Which of the following are the three properties of dataA. mean, m.pdf
 
What is the range of clinical signssymptoms of C. difficile infecti.pdf
What is the range of clinical signssymptoms of C. difficile infecti.pdfWhat is the range of clinical signssymptoms of C. difficile infecti.pdf
What is the range of clinical signssymptoms of C. difficile infecti.pdf
 
What was Kants ideas regarding retributive punishmentSolution.pdf
What was Kants ideas regarding retributive punishmentSolution.pdfWhat was Kants ideas regarding retributive punishmentSolution.pdf
What was Kants ideas regarding retributive punishmentSolution.pdf
 
What are the major events that occur during each stage in the life cy.pdf
What are the major events that occur during each stage in the life cy.pdfWhat are the major events that occur during each stage in the life cy.pdf
What are the major events that occur during each stage in the life cy.pdf
 
What challenges do corporations face with regards to social media.pdf
What challenges do corporations face with regards to social media.pdfWhat challenges do corporations face with regards to social media.pdf
What challenges do corporations face with regards to social media.pdf
 
There are no organs for excretion and gas exchange in cnidarians. How.pdf
There are no organs for excretion and gas exchange in cnidarians. How.pdfThere are no organs for excretion and gas exchange in cnidarians. How.pdf
There are no organs for excretion and gas exchange in cnidarians. How.pdf
 
the term with the definition. Duality Of Effects Journal Entry An amo.pdf
the term with the definition. Duality Of Effects Journal Entry An amo.pdfthe term with the definition. Duality Of Effects Journal Entry An amo.pdf
the term with the definition. Duality Of Effects Journal Entry An amo.pdf
 
Two proteins are normally found in the cytosol. They are involved in .pdf
Two proteins are normally found in the cytosol. They are involved in .pdfTwo proteins are normally found in the cytosol. They are involved in .pdf
Two proteins are normally found in the cytosol. They are involved in .pdf
 
Two components operate in parallel in a device, so the device fails .pdf
Two components operate in parallel in a device, so the device fails .pdfTwo components operate in parallel in a device, so the device fails .pdf
Two components operate in parallel in a device, so the device fails .pdf
 
That assignment had 2 part. I already complated part 1. and collecte.pdf
That assignment had 2 part. I already complated part 1. and collecte.pdfThat assignment had 2 part. I already complated part 1. and collecte.pdf
That assignment had 2 part. I already complated part 1. and collecte.pdf
 
Book Fundamental of Biostatistics 7th editionProblem pg. 67 #3.1.pdf
Book Fundamental of Biostatistics 7th editionProblem pg. 67 #3.1.pdfBook Fundamental of Biostatistics 7th editionProblem pg. 67 #3.1.pdf
Book Fundamental of Biostatistics 7th editionProblem pg. 67 #3.1.pdf
 
Stre cell Tran and Homeostasis 5. special proteins in the membrane th.pdf
Stre cell Tran and Homeostasis 5. special proteins in the membrane th.pdfStre cell Tran and Homeostasis 5. special proteins in the membrane th.pdf
Stre cell Tran and Homeostasis 5. special proteins in the membrane th.pdf
 
Let X and Y be two continuous random variables with probability dens.pdf
Let X and Y be two continuous random variables with probability dens.pdfLet X and Y be two continuous random variables with probability dens.pdf
Let X and Y be two continuous random variables with probability dens.pdf
 
Many areas of the country have reservoirs or waterways with locks an.pdf
Many areas of the country have reservoirs or waterways with locks an.pdfMany areas of the country have reservoirs or waterways with locks an.pdf
Many areas of the country have reservoirs or waterways with locks an.pdf
 

Recently uploaded

IGCSE Biology Chapter 14- Reproduction in Plants.pdf
IGCSE Biology Chapter 14- Reproduction in Plants.pdfIGCSE Biology Chapter 14- Reproduction in Plants.pdf
IGCSE Biology Chapter 14- Reproduction in Plants.pdf
Amin Marwan
 
math operations ued in python and all used
math operations ued in python and all usedmath operations ued in python and all used
math operations ued in python and all used
ssuser13ffe4
 
ZK on Polkadot zero knowledge proofs - sub0.pptx
ZK on Polkadot zero knowledge proofs - sub0.pptxZK on Polkadot zero knowledge proofs - sub0.pptx
ZK on Polkadot zero knowledge proofs - sub0.pptx
dot55audits
 
Beyond Degrees - Empowering the Workforce in the Context of Skills-First.pptx
Beyond Degrees - Empowering the Workforce in the Context of Skills-First.pptxBeyond Degrees - Empowering the Workforce in the Context of Skills-First.pptx
Beyond Degrees - Empowering the Workforce in the Context of Skills-First.pptx
EduSkills OECD
 
Main Java[All of the Base Concepts}.docx
Main Java[All of the Base Concepts}.docxMain Java[All of the Base Concepts}.docx
Main Java[All of the Base Concepts}.docx
adhitya5119
 
Gender and Mental Health - Counselling and Family Therapy Applications and In...
Gender and Mental Health - Counselling and Family Therapy Applications and In...Gender and Mental Health - Counselling and Family Therapy Applications and In...
Gender and Mental Health - Counselling and Family Therapy Applications and In...
PsychoTech Services
 
Film vocab for eal 3 students: Australia the movie
Film vocab for eal 3 students: Australia the movieFilm vocab for eal 3 students: Australia the movie
Film vocab for eal 3 students: Australia the movie
Nicholas Montgomery
 
Hindi varnamala | hindi alphabet PPT.pdf
Hindi varnamala | hindi alphabet PPT.pdfHindi varnamala | hindi alphabet PPT.pdf
Hindi varnamala | hindi alphabet PPT.pdf
Dr. Mulla Adam Ali
 
Temple of Asclepius in Thrace. Excavation results
Temple of Asclepius in Thrace. Excavation resultsTemple of Asclepius in Thrace. Excavation results
Temple of Asclepius in Thrace. Excavation results
Krassimira Luka
 
Chapter wise All Notes of First year Basic Civil Engineering.pptx
Chapter wise All Notes of First year Basic Civil Engineering.pptxChapter wise All Notes of First year Basic Civil Engineering.pptx
Chapter wise All Notes of First year Basic Civil Engineering.pptx
Denish Jangid
 
Advanced Java[Extra Concepts, Not Difficult].docx
Advanced Java[Extra Concepts, Not Difficult].docxAdvanced Java[Extra Concepts, Not Difficult].docx
Advanced Java[Extra Concepts, Not Difficult].docx
adhitya5119
 
BÀI TẬP DẠY THÊM TIẾNG ANH LỚP 7 CẢ NĂM FRIENDS PLUS SÁCH CHÂN TRỜI SÁNG TẠO ...
BÀI TẬP DẠY THÊM TIẾNG ANH LỚP 7 CẢ NĂM FRIENDS PLUS SÁCH CHÂN TRỜI SÁNG TẠO ...BÀI TẬP DẠY THÊM TIẾNG ANH LỚP 7 CẢ NĂM FRIENDS PLUS SÁCH CHÂN TRỜI SÁNG TẠO ...
BÀI TẬP DẠY THÊM TIẾNG ANH LỚP 7 CẢ NĂM FRIENDS PLUS SÁCH CHÂN TRỜI SÁNG TẠO ...
Nguyen Thanh Tu Collection
 
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
PECB
 
RHEOLOGY Physical pharmaceutics-II notes for B.pharm 4th sem students
RHEOLOGY Physical pharmaceutics-II notes for B.pharm 4th sem studentsRHEOLOGY Physical pharmaceutics-II notes for B.pharm 4th sem students
RHEOLOGY Physical pharmaceutics-II notes for B.pharm 4th sem students
Himanshu Rai
 
UGC NET Exam Paper 1- Unit 1:Teaching Aptitude
UGC NET Exam Paper 1- Unit 1:Teaching AptitudeUGC NET Exam Paper 1- Unit 1:Teaching Aptitude
UGC NET Exam Paper 1- Unit 1:Teaching Aptitude
S. Raj Kumar
 
How to Setup Warehouse & Location in Odoo 17 Inventory
How to Setup Warehouse & Location in Odoo 17 InventoryHow to Setup Warehouse & Location in Odoo 17 Inventory
How to Setup Warehouse & Location in Odoo 17 Inventory
Celine George
 
The basics of sentences session 6pptx.pptx
The basics of sentences session 6pptx.pptxThe basics of sentences session 6pptx.pptx
The basics of sentences session 6pptx.pptx
heathfieldcps1
 
Présentationvvvvvvvvvvvvvvvvvvvvvvvvvvvv2.pptx
Présentationvvvvvvvvvvvvvvvvvvvvvvvvvvvv2.pptxPrésentationvvvvvvvvvvvvvvvvvvvvvvvvvvvv2.pptx
Présentationvvvvvvvvvvvvvvvvvvvvvvvvvvvv2.pptx
siemaillard
 
clinical examination of hip joint (1).pdf
clinical examination of hip joint (1).pdfclinical examination of hip joint (1).pdf
clinical examination of hip joint (1).pdf
Priyankaranawat4
 
Leveraging Generative AI to Drive Nonprofit Innovation
Leveraging Generative AI to Drive Nonprofit InnovationLeveraging Generative AI to Drive Nonprofit Innovation
Leveraging Generative AI to Drive Nonprofit Innovation
TechSoup
 

Recently uploaded (20)

IGCSE Biology Chapter 14- Reproduction in Plants.pdf
IGCSE Biology Chapter 14- Reproduction in Plants.pdfIGCSE Biology Chapter 14- Reproduction in Plants.pdf
IGCSE Biology Chapter 14- Reproduction in Plants.pdf
 
math operations ued in python and all used
math operations ued in python and all usedmath operations ued in python and all used
math operations ued in python and all used
 
ZK on Polkadot zero knowledge proofs - sub0.pptx
ZK on Polkadot zero knowledge proofs - sub0.pptxZK on Polkadot zero knowledge proofs - sub0.pptx
ZK on Polkadot zero knowledge proofs - sub0.pptx
 
Beyond Degrees - Empowering the Workforce in the Context of Skills-First.pptx
Beyond Degrees - Empowering the Workforce in the Context of Skills-First.pptxBeyond Degrees - Empowering the Workforce in the Context of Skills-First.pptx
Beyond Degrees - Empowering the Workforce in the Context of Skills-First.pptx
 
Main Java[All of the Base Concepts}.docx
Main Java[All of the Base Concepts}.docxMain Java[All of the Base Concepts}.docx
Main Java[All of the Base Concepts}.docx
 
Gender and Mental Health - Counselling and Family Therapy Applications and In...
Gender and Mental Health - Counselling and Family Therapy Applications and In...Gender and Mental Health - Counselling and Family Therapy Applications and In...
Gender and Mental Health - Counselling and Family Therapy Applications and In...
 
Film vocab for eal 3 students: Australia the movie
Film vocab for eal 3 students: Australia the movieFilm vocab for eal 3 students: Australia the movie
Film vocab for eal 3 students: Australia the movie
 
Hindi varnamala | hindi alphabet PPT.pdf
Hindi varnamala | hindi alphabet PPT.pdfHindi varnamala | hindi alphabet PPT.pdf
Hindi varnamala | hindi alphabet PPT.pdf
 
Temple of Asclepius in Thrace. Excavation results
Temple of Asclepius in Thrace. Excavation resultsTemple of Asclepius in Thrace. Excavation results
Temple of Asclepius in Thrace. Excavation results
 
Chapter wise All Notes of First year Basic Civil Engineering.pptx
Chapter wise All Notes of First year Basic Civil Engineering.pptxChapter wise All Notes of First year Basic Civil Engineering.pptx
Chapter wise All Notes of First year Basic Civil Engineering.pptx
 
Advanced Java[Extra Concepts, Not Difficult].docx
Advanced Java[Extra Concepts, Not Difficult].docxAdvanced Java[Extra Concepts, Not Difficult].docx
Advanced Java[Extra Concepts, Not Difficult].docx
 
BÀI TẬP DẠY THÊM TIẾNG ANH LỚP 7 CẢ NĂM FRIENDS PLUS SÁCH CHÂN TRỜI SÁNG TẠO ...
BÀI TẬP DẠY THÊM TIẾNG ANH LỚP 7 CẢ NĂM FRIENDS PLUS SÁCH CHÂN TRỜI SÁNG TẠO ...BÀI TẬP DẠY THÊM TIẾNG ANH LỚP 7 CẢ NĂM FRIENDS PLUS SÁCH CHÂN TRỜI SÁNG TẠO ...
BÀI TẬP DẠY THÊM TIẾNG ANH LỚP 7 CẢ NĂM FRIENDS PLUS SÁCH CHÂN TRỜI SÁNG TẠO ...
 
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
 
RHEOLOGY Physical pharmaceutics-II notes for B.pharm 4th sem students
RHEOLOGY Physical pharmaceutics-II notes for B.pharm 4th sem studentsRHEOLOGY Physical pharmaceutics-II notes for B.pharm 4th sem students
RHEOLOGY Physical pharmaceutics-II notes for B.pharm 4th sem students
 
UGC NET Exam Paper 1- Unit 1:Teaching Aptitude
UGC NET Exam Paper 1- Unit 1:Teaching AptitudeUGC NET Exam Paper 1- Unit 1:Teaching Aptitude
UGC NET Exam Paper 1- Unit 1:Teaching Aptitude
 
How to Setup Warehouse & Location in Odoo 17 Inventory
How to Setup Warehouse & Location in Odoo 17 InventoryHow to Setup Warehouse & Location in Odoo 17 Inventory
How to Setup Warehouse & Location in Odoo 17 Inventory
 
The basics of sentences session 6pptx.pptx
The basics of sentences session 6pptx.pptxThe basics of sentences session 6pptx.pptx
The basics of sentences session 6pptx.pptx
 
Présentationvvvvvvvvvvvvvvvvvvvvvvvvvvvv2.pptx
Présentationvvvvvvvvvvvvvvvvvvvvvvvvvvvv2.pptxPrésentationvvvvvvvvvvvvvvvvvvvvvvvvvvvv2.pptx
Présentationvvvvvvvvvvvvvvvvvvvvvvvvvvvv2.pptx
 
clinical examination of hip joint (1).pdf
clinical examination of hip joint (1).pdfclinical examination of hip joint (1).pdf
clinical examination of hip joint (1).pdf
 
Leveraging Generative AI to Drive Nonprofit Innovation
Leveraging Generative AI to Drive Nonprofit InnovationLeveraging Generative AI to Drive Nonprofit Innovation
Leveraging Generative AI to Drive Nonprofit Innovation
 

Use De Moivres theorem to change the given complex number to the fo.pdf

  • 1. Use De Moivre's theorem to change the given complex number to the form a + bi, where a and b are real numbers. (- Squareroot 3/2 - 1/2 i)^4 Solution ( -sqrt3/2 -i/2)^4 Polar form = r*e^i*theta r = sqrt[ (-sqrt3/2)^2 + (1/2)^2 )] = 1 theta = tan^-1(-1/2 /-sqrt3/2) = pi +pi/3 = 4pi/3 ( -sqrt3/2 -i/2)^4 = (re^i*theta)^4 = r^4e^i*4theta = 1*e^i*16pi/3 = cos16pi/3 + isin16pi/3 = -0.5 -i*0.866