Question

How do you use the binomial theorem to expand `(-1/2+sqrt3/2i)^3`?

Answer 1

The answer `=1`

Explanation:

Normally, you don't need the binomial theorem but Euler's Identity and Demoivre's Theorem

`i^2=-1`

So, by the binomial theorem

`(-1/2+sqrt3/2i)^3=(-1/2)^3+3(-1/2)^2(sqrt3/2i)+3(-1/2)(sqrt3 /2i)^2+(sqrt3/2i)^3`

`=-1/8+(3sqrt3)/8i+9/8-(3sqrt3)/3i`

`=1`