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Complex Numbers and Quadratic Equations — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsComplex Numbers and Quadratic Equations1 Mark
MCQ
The value of $(\text{z}+3)(\bar{\text{z}}+3)$ is equivalent to:
  • ✓
    $|z + 3|^2$
  • B
    $|z - 3|$
  • C
    $z^2 + 3$
  • D
    None of these.
✓

Answer

Correct option: A.
$|z + 3|^2$
$|z + 3|^{2}$
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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