Question

Find the smallest integer n such that $\frac{(1+i{)}^n}{(1-i{)}^n}$ is $1$

• A. $3$
• B. $1$
• C. $2$
• D. $4$

Answer 1

The correct option is D $4$

Here we use a little trick. We have $\frac{1}{i}=\frac{1}{i}\times \frac{i}{i}$

Remember that $i\times i=-1$ and therefore we have, $\frac{1}{i}\times \frac{i}{i}=-i$.

Hence using it in the denominator of the given equation, we have: $\frac{(1+i{)}^n}{\left(\right(1+i)/i{)}^n}=(i{)}^n$. Hence, for $(i{)}^n=1$, $n$ should be atleast $4$.