Question

The value of ${\left(1+i\right)}^8+{\left(1-i\right)}^8$ is

• A. $16$
• B. $-16$
• C. $32$
• D. $-32$

Answer 1

The correct option is C $32$

$(1+i{)}^8+(1-i{)}^8$

$={\left\{\right(1+i{)}^2\}}^4+{\left\{\right(1-i{)}^2\}}^4$

$={\left\{\right(1+2i-1\left)\right\}}^4+{\left\{\right(1-2i-1\left)\right\}}^4$

$=(2i{)}^4+16(i{)}^4$

$=16+16$

$=32$