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

• Complex Numbers

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

1. x = 4n, where n is any positive integer.
2. x = 2n, where n is any positive integer.
3. x = 4n + 1, where n is any positive integer.
4. x = 2n + 1, where n is any positive integer.

Solution

[(1 + i)/(1 - i)]^x = 1

[(1 + i)(1 + i)/(1 - i)(1 + i)]^x = 1

[(1 + i² + 2i)/(1 - i²)]^x = 1

i² = -1

(2i/2)^x = 1

i^x = 1

i^x = i⁴ⁿ

x = 4n

The correct option is A.