Femtobytes
Problem type

Power of a complex number with De Moivre's theorem

What it solves
Raise a complex number to a whole-number power by going through polar form, where a power becomes one multiplication of the angle, and confirm the answer by multiplying the long way in exact arithmetic.
Subject
Complex Numbers
Topic
Length and angle
Also called
De Moivre, power of a complex number, raise to a power
Your problem

Work out this power and give the answer in the form a+bia + bi.

(1+3i)5\left( 1 + \sqrt{3} i \right)^{5}
Invent a new one: