Question

How do I find the polar form of `3sqrt2 - 3sqrt2i`?

Answer 1

Polar form is `6(cos(-pi/4)+isin(-pi/4))`

Explanation:

First just find the absolute value of the complex number. We have it as `3sqrt2-3sqrt2i` and its absolute value is

`sqrt((3sqrt2)^2+(-3sqrt2)^2)=sqrt(18+18)=sqrt36=6`

Hence number can be written as

`6((3sqrt2)/6-(3sqrt2)/6i)`

or `6(1/sqrt2-1/sqrt2i)`

As polar number is of the form `r(costheta+isintheta)`

we have `r=6` and `costheta=1/sqrt2` and `sintheta=-1/sqrt2`

As cosine is ratio is positive and sine ratio is negative,

`theta=pi/4`

Hence, polar form is `6(cos(-pi/4)+isin(-pi/4))`