Question

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

• A. $8$
• B. $8i$
• C. $-8$
• D. $32$

Answer 1

The correct option is C $-8$

$(1+i{)}^4+(1-i{)}^4$

$\Rightarrow$ $\left[\right(1+i{)}^2{]}^2+\left[\right(1-i{)}^2{]}^2$

We know, $(a+b{)}^2=a^2+2ab+b^2$ and $(a-b{)}^2{=}^2-2ab+b^2$

$\Rightarrow$ $[1+2i+i^2{]}^2+[1-2i+i^2{]}^2$

$\Rightarrow$ $[1+2i-1{]}^2+[1-2i-1{]}^2$ [ $i^2=-1$ ]

$\Rightarrow$ $(2i{)}^2+(-2i{)}^2$

$\Rightarrow$ $4i^2+4i^2$

$\Rightarrow$ $-4-4$

$\Rightarrow$ $-8$

$\therefore$ $(1+i{)}^4+(1-i{)}^4=-8$