Complex Number Presentation By : Anum Urooj

1. Starts in the
name of
ALLAH

2. PRESENTATION BY
ANUM UROOJ Cs (104)
Superior Group Of Colleges

3. Complex numbers

4. What is
Complex
Numbers?
Modulus Conjugate
Polar Form
De Moivre's
Theorm Subtraction
Multiplication
Addition
DivisionApplication
COMPLEX
NUMBERS

5. Complex numbers
Real part Imaginary part
 It can be written in the form :
Z = a + bi
A complex numbers is a number consisting a
Real and Imaginary part.

6. COMPLEX NUMBERS
• SUBSETS
Real numbers and imaginary
numbers are the subsets of
the complex numbers

7. • Power of "i"
The power of i in complex
numbers is equal to under root of
negative one , can be written as
COMPLEX NUMBERS

8. COMPLEX NUMBERS
1. Real part "a" is drawn at x-axis
that is on vertically.
2. Imaginary part "b" is drawn at
y- axis that is on horizontally.
• Graphically Representation:

9. COMPLEX CONJUGATE
• The complex conjugate of complex number Z = a + bi, is
denoted by
The complex number and its conjugate have the same real part.
Re(a) = Re ( )
The sign of the imaginary part of the conjugate complex is reversed.
Im(b) = Im -( )
Z = a - bi

10. COMPLEX CONJUGATE
• Graphicall Representaion
The conjugate is drawn at
downward to Imaginary part
that is downward to the x-
axis

11. Complex Modulus
• The modulus or magnitude of Z
denoted by IZ , is the distance
from the origin to the point (a,b).

12. Complex numbers
• Equal complex numbers
Two complex numbers are equal if their real parts are equal and
their imaginary parts are equal.
If a + bi = c + di,
Then,
a = c and b = c

13. ADDITION OF COMPLEX NUMBERS
• If a + bi and c + di are two complex numbers then addition of
complex numbers are ,
(a + bi) + (c + di) = (a + c) + (b + d)i
• Example:
(2 + 4i) + (5 + 3i)
= (2 + 5) + (4 + 3)i
= 7 + 7i

14. Subtraction of
complex
numbers
• If a + bi and c + di are two complex
numbers then subtraction of
complex numbers are
(a + bi) - (c + di) = (a - c) + (b - d)i
• Example:
(3 + 2i) - (1+3i)
= (3 - 1) + (2 - 3)i
= 2 -1i
= 2 - i

15. Multiplication of
complex numbers • If a +bi and c + di are two
complex numbers
multiplication of two complex
numbers is
(a + bi)(c + di) = (ac -bd) + ( ad + bc)i
• Example:
(2 + 3i)(4 + 5i)
= (2x4 - 2x5) + (3x4 - 3x5)i
= (8 - 10) + (12 - 15)i
= -2 - 3i

16. DIVISION OF A COMPLEX NUMBERS
• If a + bi and c + di are two complex numbers then division of a
complex numbers are
• Example:

17. EXPRESSING COMPLEX NUMBERS IN POLAR FORM
x = r cos 0 y = r sin 0
Z = r ( cos 0 + i sin 0 )

18. DE MOIVRE'S THEORM
DE MOIVRE'S THEORM is the theorm which show us
how to take complex number to any power easily.

19. APPLICATIONS
• COMPLEX NUMBERS HAVE MANY APPLICATION IN
SCIENCE, MATHEMATICS, ENGINEERING, STATICS ETC.
The complex equation is a basic formula used for designing air foils-
airplane wings and Figuring out flow forces around a circular object in
water for instance
A complex numbers could be used to represent the position of an
object in a two dimentional plane
A complex number is used in solving diffrent equations with
function of complex root

20. ANY QUESTION ??

21. Thankyou for your attention