Question

If n is a positive integer, then ${\left(\frac{1+i}{1-i}\right)}^{4n+1}$ =

• A. 1
• B. -1
• C. i
• D. -i

Answer 1

The correct option is C i

Since $\frac{1+i}{1-i}=\frac{(1+i)(1+i)}{(1-i)(1+i)}=i$
Therefore ${\left(\frac{1+i}{1-i}\right)}^{4n+1}=i^{4n+1}=i{i}^{4n}=i(\because i^{4n}=1)$