Question

If a = 1 + i, then a² equals
(a) 1 − i
(b) 2i
(c) (1 + i) (1 − i)
(d) i − 1.

Answer 1

(b) 2i

a = 1 + i
On squaring both the sides, we get,
a² = (1 + i)²
$\Rightarrow$a² = 1 + i² + 2i
$\Rightarrow$a² = 1$-$1 + 2i ($\because$ i² = $-$1)
$\Rightarrow$a² = 2i