Write the following numbers in the polar form

Question

Write the following numbers in the polar form re^iθ, 0≤θ<2π

a) 1/9

r=

θ= 

b)6+6i

r=

θ=

c)-3-31

r=

θ=

 

 

Answer 1

a)  1/9 eⁱ⁽⁰⁾

 

   r = 1/9 

 

   Θ = 0°

 

 b)

 

      6 + 6i

 

     r = √( 6^2 + 6 ^2) = √72 = 6 √2

   

      θ = tan^-1 ( 6/6=1) = ∏/4 

 

      6√2 e^i∏/4

 

    d) - 3 - 3i

 

        r = √( 3^2 + 3^2) = 3√2

        θ = tan^-1( -3/ -3) = 5π/4

        

         3√2 e^i5∏/4