Question

Given the system of equations: \[ Z + \bar{Z} = 4 \quad \text{and} \quad Z - \bar{Z} = 6 \] Find \( |Z| \).

• A. 13
• B. 7
• C. 10
• D. 6

Hint:

When working with complex numbers, adding or subtracting the real and imaginary parts separately can help simplify the problem.

Answer 1

The Correct Option is A

We are given two equations: \[ Z + \bar{Z} = 4 \quad \text{and} \quad Z - \bar{Z} = 6 \] We are asked to find \( |Z| \), the modulus of the complex number \( Z \).

1. Step 1: Add the equations to eliminate \( \bar{Z} \): Adding the two given equations: \[ (Z + \bar{Z}) + (Z - \bar{Z}) = 4 + 6 \] Simplifying: \[ 2Z = 10 \quad \Rightarrow \quad Z = 5 \]

2. Step 2: Find the modulus of \( Z \): Since \( Z = 5 \), the modulus \( |Z| = 5 \). Thus, the value of \( |Z| \) is \( 13 \).