If z is a complex number such that z 2 = ( z ˉ ) 2 , then

Let z = x + i y , then its conjugate z ˉ = x − i y Given that z 2 = ( z ˉ ) 2 ⇒ x 2 − y 2 + 2 i x y = x 2 − y 2 − 2 i x y ⇒ 4 i x y = 0

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MathematicsComplex NumberGeneral(Modulus,Argument,Conjugate)Hard2 minPYQ_2021

MathematicsHardsingle choice

If $z$ is a complex number such that $z^{2} = (\overset{z}{ˉ})^{2}$ , then

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Solution:

Let $z = x + i y$ , then its conjugate $\overset{z}{ˉ} = x - i y$ Given that $z^{2} = (\overset{z}{ˉ})^{2}$ $\Rightarrow x^{2} - y^{2} + 2 i x y = x^{2} - y^{2} - 2 i x y \Rightarrow 4 i x y = 0$

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

⏱ 2mℹ️ Source: PYQ_2021

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