Question

Express 1/((1-i√3)^3) in the form a/b where a,b are integers.

I've attempted this question but I ended up with a complex number for a, whereas the question wants integers. How do I do it?

Answer 1

\[\frac{ 1 }{ (1-i \sqrt{3})^{3} }\] is the expression, I realised it's quite hard to see in the text form.

Answer 2

if you look at just the denominator, you have:\[1-i\sqrt{3}\]if you re-arrange this as follows:\[2(\frac{1}{2}-i\frac{\sqrt{3}}{2})\]then you should be able to see how to convert this into the form \(e^{i\theta}=\cos(\theta)+i\sin(\theta)\).
This re-arrangement should make it easier to evaluate.