Question

Find the value of \( Z^2 \) if \( Z = \left( 1 + \frac{1}{i} \right) \).

• A. 4
• B. 5
• C. 6
• D. 3

Hint:

When squaring complex numbers, remember to apply the distributive property and simplify terms involving \( i^2 = -1 \).

Answer 1

The Correct Option is A

We are given: \[ Z = 1 + \frac{1}{i} \] To simplify \( Z \), we know that \( \frac{1}{i} = -i \), so: \[ Z = 1 - i \] Now, we need to find \( Z^2 \): \[ Z^2 = (1 - i)^2 = 1^2 - 2 \times 1 \times i + (-i)^2 \] \[ Z^2 = 1 - 2i - 1 = -2i \] Thus, \( Z^2 = -2i \), so the correct answer is \( 4 \).