Question

The value of $(1+i{)}^{2002}$ is

• A. a purely real number
• B. Purely imaginary number
• C. Has both real & imaginary parts
• D. None of these

Answer 1

The correct option is B

Purely imaginary number

$(1+i{)}^{2002}$ = $\left[\right(1+i{)}^2{]}^{1001}$ = $[2i{]}^{1001}$

$2^{1001}$ . $i^{1001}$

= i.$2^{1001}$