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If $z \neq 0$ is s a complex number such that $\arg (z) = π / 4$ then

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Re⁡z2=0

Im⁡z2=0

Re⁡z2=Im⁡z2

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detailed solution

Correct option is A

As arg⁡(z)=π/4 we can writez=rcos⁡π4+isin⁡π4where r=|z|⇒ z2=r2cos⁡π2+isin⁡π2 [Using De Moivre’s Theorem] =r2(0+i)=ir2⇒ Re⁡z2=0

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If z≠0 is s a complex number such that arg⁡(z)=π/4 then

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If $z \neq 0$ is s a complex number such that $\arg (z) = π / 4$ then