Ask Uncle Colin: Powers and polar form | Colin

Ask Uncle Colin is a chance to ask your burning, possibly embarrassing, maths questions — and to show off your skills at coming up with clever acronyms. Send your questions to colin@flyingcoloursmaths.co.uk and Uncle Colin will do what he can.

Dear Uncle Colin,

I’ve been given $u = (2\sqrt{3} – 2\i)^6$ and been told to express it in polar form. I’ve got as far as $u=54 -2\i^6$, but don’t know where to take it from there!

– Not A Problem I’m Expecting to Resolve

Hello, NAPIER, and thanks for your message!

I fear you’ve fallen into one of the classical mathematical traps: you…