Question

If `((1 + i)/(1 - i))^x` = 1, then ______.

Options

• x = 2n + 1

• x = 4n

• x = 2n

• x = 4n + 1, where n ∈ N

Answer 1

If `((1 + i)/(1 - i))^x` = 1, then x = 4n.

Explanation:

Given that: `((1 + i)/(1 - i))^x` = 1

⇒ `(((1 + i)(1 + i))/((1 - i)(1 - i)))^x` = 1

⇒ `((1 + i^2 + 2i)/(1 - i^2))^x` = 1

⇒ `((1 - 1 + 2i)/(1 + 1))^x` = 1

⇒ `((2i)/2)^x` = 1

⇒ (i)^x = (i)⁴ⁿ

⇒ x = 4n, n ∈ N