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Parametric Equations

Polar Coordinates

Polar Form of Complex Numbers

Mult. & Div. of Complex No's

Powers & Roots

Summary&Test

 

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 UNIT 12  :  PARAMETRIC EQUATIONS AND POLAR COORDINATES

 LESSON 6: SUMMARY & TEST

 

LESSON 1:  PARAMETRIC EQUATIONS DEFINED

 

 

   

 

-2

-2 + 1 = -1  

2(-2)2 + 3=11

(-1, 11)

-1

-1 + 1 = 0

2(-1)2 + 3 = 5

(0, 5)

0

0 + 1 = 1

2(0)2 + 3 = 3

(1, 3)

1

1 + 1 = 2

2(1)2 + 3 = 5

(2, 5)

2

2 + 1 = 3

2(2)2 + 3 = 11

(3, 11)

3

3 + 1 = 4

2(3)2 + 3 = 21

(4, 21)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

LESSON 2:

 

Converting Between Polar and Rectangular Form.

 

 

 

 

 

 LESSON 3:  POLAR FORM OF COMPLEX NUMBERS

 

 

Converting Between Polar and Rectangular Form of Complex Numbers

 

 

 

 

 

 

LESSON 4:  MULTIPLICATION AND DIVISION OF COMPLEX NUMBERS IN POLAR FORM

 

Text Box: Theorem 1:  
 
To find the product of two complex numbers in polar form , multiply their moduli (radii)  and add their arguments.
 

 

 

 

 

 

 

 

 

Text Box: Theorem 2:  
 
To find the quotient of two complex numbers in polar form , divide their moduli (radii)  and subtract their arguments.
 

 

 

 

 

 

 

 

 


 

 

 

 

 LESSON 5:  POWERS AND ROOTS OF COMPLEX NUMBERS

 

 

Powers and roots of complex numbers can be calculated using De Moivre’s theorem given below.

 

 

Text Box: De Moivres Theorem :
 

 

 

 

 

 

 

 


 

 

 

 

 

 

 

 

 

 

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