analysis - Real and imaginary part of $(1-isqrt{3})^6$

i am a bit stuck here.

As the title says i try to find out how to write complex numbers like for example

$$(1-i\sqrt{3})^6$$ in the normal representation $$z = x + i*y$$
I already found out that the polar representation of complex numbers will come in handy here, but i can't make the conclusion at the moment.

How can i get from here to the polar representation? How do i get the real and imaginary part from the polar representation? If you have a hint, can you please just leave a quick post here, thanks.

Answer

The modulus of $1-i\sqrt{3}$ is $\sqrt{1+3}=2$, so you can write

$$1-i\sqrt{3}=2\left(\frac{1}{2}-i\frac{\sqrt{3}}{2}\right) = 2(\cos(-\pi/3)+i\sin(-\pi/3))$$
Can you compute the sixth power, now?