Question

Convert 3 - 3i to polar form.

Answer 1

Answer:

Option d is correct that is $z=\sqrt{18} cos(\frac{7\pi}{4})+i sin(\frac{7\pi}{4})$

Step-by-step explanation:

We have been given a complex number 3-3i we have to convert it in the polar form:

polar form of a complex number:

$z=r(cos{\theta}+i sin{\theta})$

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

the general form of complex number is:

x+iy

Here, x=3 and y=-3

Hence, $r=\sqrt{3^2+(-3)^2}=\sqrt{18}$

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

   $\theta=tan^{-1}\frac{-3}{3}$

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

$\Rightarrow \theta=2{\pi}-\frac{\pi}{4}$

$\Rightarrow \theta=\frac{7\pi}{4}$

Hence, substituting all the values in polar form formula we get:

$z=\sqrt{18} cos(\frac{7\pi}{4})+i sin(\frac{7\pi}{4})$

Therefore, option d is correct.