Question

if n is an odd integer, $i=\sqrt{-1}$ then $(1+i{)}^{6n}+(1-i{)}^{6n}$ is equal to

• A. $0$
• B. $2$
• C. $-2$
• D. none of these

Answer 1

The correct option is A $0$

The above expression can be simplified as
$2^{3n}[e^{\frac{i6n\pi }{4}}+e^{\frac{-6n\pi i}{4}}]$
$=2^{3n}[e^{\frac{3n\pi .i}{2}}+e^{\frac{-3n\pi .i}{2}}]$
Hence if n is odd, we get
$=2^{3n}[i-i]$
$=0$