JEE Mains · Maths · STD 11 - 4.1 complex nubers
If \(z=x+i y, x y \neq 0\), satisfies the equation \(z^2+i \bar{z}=0\), then \(\left|z^2\right|\) is equal to :
- A \(9\)
- B \(1\)
- C \(4\)
- D \(\frac{1}{4}\)
Answer & Solution
Correct Answer
(B) \(1\)
Step-by-step Solution
Detailed explanation
\( z^2=-i \bar{z} \) \( \left|z^2\right|=|i \bar{z}|\) \( \left|z^2\right|=|z|\) \( |z|^2-|z|=0\) \( |z|(|z|-1)=0\) \( |z|=0 \text { (not acceptable) } \) \( \therefore|z|=1 \) \( \therefore|z|^2=1\)
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