Choose the correct answer. The value of (z+3)( z +3) is equivalen… - Vidyadip

MCQ

Choose the correct answer.
The value of $(\text{z}+3)(\bar{\text{z}}+3)$ is equivalent to:

A
|z + 3|²
B
|z - 3|
C
z² + 3
D
None of these.

✓

Answer

|z + 3|²

Solution:

Let z = x + iy. Then

$(\text{z}+3)(\bar{\text{z}}+3)=(\text{x}+\text{iy}+3)(\text{x}-\text{iy}+3)$

$=(\text{x}+3)^2-(\text{iy})^2$

$=(\text{x}+3)^2+\text{y}^2$

$=|\text{x}+3+\text{iy}|^2=|\text{z}+3|^2$

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