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. $1$

Answer 1

The correct option is A $0$

As, $(1+i{)}^{6n}+(1-i{)}^{6n}=\left[\right(1+i{)}^2{]}^{3n}+\left[\right(1-i{)}^2{]}^{3n}$
$=(2i{)}^{3n}+(-2i{)}^{3n}$ , as $n$ is odd
$=(2i{)}^{3n}-(2i{)}^{3n}$
$=0$