Question

The value of $(1+i{)}^4+(1-i{)}^4$ is

• A. 8
• B. 4
• C. -8
• D. -4

Answer 1

The correct option is C

-8

$\text{Using}{a}^4+b^4=(a^2+b^2{)}^2-2a^2{b}^2(1+i{)}^4+(1-i{)}^4=((1+i{)}^2+(1-i{)}^2{)}^2-2(1+i{)}^2(1-i{)}^2=(1+i^2+2i+1+i^2-2i{)}^2-2(1+i^2+2i\left)\right(1+i^2-2i)=(1-1+2i+1-1-2i{)}^2-2(1-1+2i)(1-1-2i)=\left(0\right)-2\left(2i\right)(-2i)(\because i^2=-1)=8i^2=-8$