Question

Rewrite the rectangular form of the complex number in its equivalent polar form. Approximate all angle measures to the nearest degree.
z = 3 + 2i

Answer 1

Rectangular form of z is z = 3 +  2i

Polar form of complex number is (r , $\theta$).

In general if z = x + iy

$r = \sqrt{x^2 + y^2}$

$\theta = tan^{-1} \frac{y}{x}$

So in given complex number z = 3 + 2i

So r is
 $r = \sqrt{(3)^2 + (2)^2}$
           $= \sqrt{9 + 4 } = \sqrt{13}$

$\theta = tan^{-1} ( \frac{y}{x}) = tan^{-1} ( \frac{2}{3}}$
                  $= 33.703$ degree.

So the rectangular form is $( \sqrt{13} , 33.703$ degree ).

Answer 2

My answers have two options with sqr root of 13. Of the two which could it be?

z=sqr rt of 13(cos56 + i sin56)

z=sqr rt of 13(cos34 + i sin34)