Question

express the complex number 2 -2i into polar form

Answer 1

Answer:

The polar form of 2 - 2i is  $z=2\sqrt{2} (cos\frac{3\pi }{4}+isin\frac{3\pi }{4} )$

Step-by-step explanation:

The given complex number is z = 2 - 2i

It is in the standerd form z = a + ib where a = 2 and b = -2

The standerd polar form is z = r(cos$\theta$ + isin$\theta$)

To find r and $\theta$ consider,

$r=\sqrt{a^{2} +b^{2} }$

$r=\sqrt{2^{2} +(-2)^{2} }$

$r=2\sqrt{2}$

$\theta=tan^{-1}(\frac{b}{a} )$

$\theta=tan^{-1}(\frac{-2}{2} )$

$\theta=\frac{3\pi }{4}$

We know that z = r(cos$\theta$ + isin$\theta$)

Therefore, the polar form of 2 - 2i is

$z=2\sqrt{2} (cos\frac{3\pi }{4}+isin\frac{3\pi }{4} )$