write the following numbers in the polar form

Question

write the following numbers in the polar form re^iθ , 0≤θ<2pi

a) 1/9

r=

θ=

b)6+6i

r=

θ=

c)-3-3i

r=

θ=

 

Answer 1

a)

 

1/9 = 1/9 e⁰⁽ⁱ⁾  = 1/9 e⁰

 

 

b )

 

 6 + 6i

  r = √( 6^2 + 6^2) = 6√2

   

θ = Tan ^-1( 1) = Π/ 4

 

6 + 6i = 6 √2 e ^iΠ/4

 

  c )

 

     c)

 

       -3 - 3i

 

       r = √ (( -3) ^2  + ( -3) ^2 ) = 3√2

          

            θ = tan^-1( -3/ -3 ) = 5Π/4

 

       - 3 - 3 i = 3√2 e ^i5Π/4