Express $(1-i)^{11}$ in cartesian form. Express $(1-i)^{11}$ in cartesian form.
Apart from expanding the expression, I don't know how to do this. I've looked at the solution and still don't understand how/why it has been done.

Hint: $1-i=\sqrt 2e^{-i\pi/4}{}{}{}{}$.
To find the above equality you can think about it geometrically and use the known techniques:

Or algebraically by proving that given any $a,b\in \mathbb R$, it holds that $a+ib=\sqrt{a^2+b^2}e^{i\arg(a+ib)}$, where $$\arg(a+ib)=\begin{cases} \arctan(b/a), &\text{if }a>0\\ \pi /2, &\text{if }a=0\land b>0\\ \arctan(b/a)+\pi, &\text{if }a<0\\ -\pi/2, &\text{if }a=0\land b<0\end{cases}$$
