The other day I was speaking to my teacher about complex numbers and I was expanding something like $(2-3i)^{10}$ using binomial expansion. He said that it was probably the quickest method, but then corrected himself, hinting at a quicker way to expand it.
Anyone have any ideas what this quicker method was?
$$(2-3i)^2=-5-12i$$ and $$(-5-12i)^5=-3125-37500i+180000+432000i-518400-248832i=-341525+145668i$$ ———————————————
Addendum to answer question in comment:
Sometimes it’s easier to take powers of complex numbers by converting to polar form. For example $(1+i)^{10}=(\sqrt2e^{i\pi/4})^{10}=32e^{i\pi/2}=32i$