Question

If $n \in \mathbb{Z}$, then the expression $\frac{2^n}{(1-i)^{2n}} + \frac{(1+i)^{2n}}{2^n}$ is equal to:

• A. $2i^n$
• B. 0
• C. $2^{n+1}$
• D. $i^n$

Hint:

Remember that $(1+i)^2 = 2i$ and $(1-i)^2 = -2i$. These are very common shortcuts in complex number problems.

Answer 1

The Correct Option is A