Let z ∈ C be such that z − 2 + i z 2 + 3 i = 2 + 3 i . Then the sum of all possible values of z 2 is

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Mathematics - Complex Number Question with Solution | TestHub

MathematicsComplex NumberGeneral(Modulus,Argument,Conjugate)Easy2 minPYQ_2025

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Let $z \in C$ be such that $\frac{z ^{2} + 3 i}{z - 2 + i} = 2 + 3 i$ . Then the sum of all possible values of $z^{2}$ is

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Solution:

$z^{2} + 3 i = z (2 + 3 i) - 7 - 4 i$
$z^{2} - z (2 + 3 i) + 7 + 7 i = 0$
$z_{1}^{2} + z_{2}^{2} = (z_{1} + z_{2})^{2} - 2 z_{1} z_{2} = 4 - 9 + 12 i - 14 - 14 i = - 19 - 2 i$

Stream:JEESubject:MathematicsTopic:Complex NumberSubtopic:General(Modulus,Argument,Conjugate)

⏱ 2mℹ️ Source: PYQ_2025

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