Verified Solution • 2025–26 Session moderate

QJEEM24Mac7bf: JEE Main 2024 Mathematics - Class 11 JEEM24Mac7bf Solution: If , satisfies the equation , then is equal to :

If z=x+iy,xy≠0z=x+i y, x y \neq 0 , satisfies the equation z2+izˉ=0z^2+i \bar{z}=0 , then ∣z2∣\left|z^2\right| is equal to :

Multiple Choice Options

  • A 9
  • B 14\frac{1}{4}
  • C 4
  • D 1

Step-by-Step Verified Solution

amp;z2=−izˉamp;∣z2∣=∣izˉ∣amp;∣z2∣=∣z∣amp;∣z∣2−∣z∣=0amp;∣z∣(∣z∣−1)=0amp;∣z∣=0 (not acceptable) amp;∴∣z∣=1amp;∴∣z∣2=1\begin{aligned}& 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\end{aligned}

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