Squaring first avoids unnecessary expansion: $(2+2i)^2=8i$, and squaring again gives \b[the fourth power] $\boxed{z^4=-64}$. In the <polar form of a complex number>, $z=2\sqrt2\,e^{i\pi/4}$; multiplying its <complex argument> by four gives the same negative-real result.

Solution

Past exam of the mathematics course of the University of Cambridge / 2014 / ia / Paper 1 / 1B / a / i / Solution

 Solution (source code)