Question:
If \( z + \bar{z} = 6 \) and \( z - \bar{z} = 4i \), then \( |z|^2 = \)
If \( z + \bar{z} = 6 \) and \( z - \bar{z} = 4i \), then \( |z|^2 = \)
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Use \( z + \bar{z} = 2x \) and \( z - \bar{z} = 2iy \) to quickly extract real and imaginary parts.
Updated On: Apr 21, 2026
- \(36 \)
- \(16 \)
- \(15 \)
- \(13 \)
- \(9 \)
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The Correct Option is D
Solution and Explanation
Concept:
Let \( z = x + iy \), then:
\[
z + \bar{z} = 2x, \quad z - \bar{z} = 2iy
\]
Step 1: Find real and imaginary parts.
\[ 2x = 6 \Rightarrow x = 3 \] \[ 2iy = 4i \Rightarrow y = 2 \]
Step 2: Compute modulus squared.
\[ |z|^2 = x^2 + y^2 = 3^2 + 2^2 = 9 + 4 = 13 \]
Step 1: Find real and imaginary parts.
\[ 2x = 6 \Rightarrow x = 3 \] \[ 2iy = 4i \Rightarrow y = 2 \]
Step 2: Compute modulus squared.
\[ |z|^2 = x^2 + y^2 = 3^2 + 2^2 = 9 + 4 = 13 \]
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