Question

The smallest positive integer n for which `((1 + i)/(1 - i))^n` = –1 is ______.

Options

• 1

• 2

• 3

• 4

Answer 1

The smallest positive integer n for which `((1 + i)/(1 - i))^n` = –1 is 2.

Explanation:

`((1 + i)/(1 - i))^n = [((1 + i))/((1 - i)) xx ((1 + i))/((1 + i))]^n`

= `[(1 + i)^2/(1 + 1)]^n`

= `[(1 - 1 + 2i)/2]^n`

= (i)ⁿ

Smallest positive integer must be 2 so that `((1 + i)/(1 - i))^n` = –1   ...[∵ i² = –1]