How do you calculate (1 + i)/(1 - i)?

We’ll calculate (1 + i)/(1-i) by using i² = -1

Answer: (1 + i)/(1 − i) = i

Let see, how we can solve it using i² = -1.

Explanation: 

We have to evaluate (1 + i)/(1 − i)

We have to multiply numerator and denominator by (1 + i)

(1 + i)/(1 − i) × (1 + i)/(1 + i) = 1 + 2i + i² / 1−i²

As we know that i² = -1, so we get

= 1 + 2i − 1/ 1−(−1)

= 2i / 2

= i

Thus, (1 + i)/(1 − i) = i