Mathematic I Prepared by Dr. Sahar abdul Hadi

Polar Coordinates &Complex Algebra 1

CHAPTER SEVEN

Polar Coordinates and Complex Numbers

Polar Coordinates:

Definition of Polar Coordinates:

Mathematic I Prepared by Dr. Sahar abdul Hadi

Polar Coordinates &Complex Algebra 2

2

1 2 3

Mathematic I Prepared by Dr. Sahar abdul Hadi

Polar Coordinates &Complex Algebra 3

y

p (x,y)=

r y

Mathematic I Prepared by Dr. Sahar abdul Hadi

Polar Coordinates &Complex Algebra 4

Mathematic I Prepared by Dr. Sahar abdul Hadi

Polar Coordinates &Complex Algebra 5

Mathematic I Prepared by Dr. Sahar abdul Hadi

Polar Coordinates &Complex Algebra 6

Mathematic I Prepared by Dr. Sahar abdul Hadi

Polar Coordinates &Complex Algebra 7

Mathematic I Prepared by Dr. Sahar abdul Hadi

Polar Coordinates &Complex Algebra 8

Mathematic I Prepared by Dr. Sahar abdul Hadi

Polar Coordinates &Complex Algebra 9

Mathematic I Prepared by Dr. Sahar abdul Hadi

Polar Coordinates &Complex Algebra 10

Complex Algebra Complex Number

—

Complex Variables in Polar form

Mathematic I Prepared by Dr. Sahar abdul Hadi

Polar Coordinates &Complex Algebra 11

:

Mathematic I Prepared by Dr. Sahar abdul Hadi

Polar Coordinates &Complex Algebra 12

Mathematic I Prepared by Dr. Sahar abdul Hadi

Polar Coordinates &Complex Algebra 13

=

Mathematic I Prepared by Dr. Sahar abdul Hadi

Polar Coordinates &Complex Algebra 14

Trigonometric function

______________________________ by addition

Hyperbolic function

Mathematic I Prepared by Dr. Sahar abdul Hadi

Polar Coordinates &Complex Algebra 15

Derivatives of A complex variable:

Cauchy-Riemann conditions

Mathematic I Prepared by Dr. Sahar abdul Hadi

Polar Coordinates &Complex Algebra 16

1-

2-

3-

4-