Question

The value of $(1+i{)}^8+(1-i{)}^8$ is
[RPET 2001; KCET 2001]

• A. 16
• B. -16
• C. 32
• D. -32

Answer 1

The correct option is C 32

$\because (1+i{)}^2=1+i^2+2i=2iand(1-i{)}^2=1+i^2-2i=-2i$
$\Rightarrow (1+i{)}^8+(1-i{)}^8=(2i{)}^4+(-2i{)}^4=2^4(i^4+i^4)$
$=2^5=32.$