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Let $z$ and $w$ be two non-zero complex numbers such that $| z | = | w |$ and $\arg (z) + \arg (w) = π$ . Then $z$ equal

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Correct option is D

Let |z|=|w|=r and arg⁡(w)=θ, so that arg⁡(z)=π−θWe have z=r[cos⁡(π−θ)+isin⁡(π−θ)]=r(−cos⁡θ+isin⁡θ)=−r(cos⁡θ+isin⁡θ)=−w¯

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Let z and w be two non-zero complex numbers such that |z|=|w|andarg⁡(z)+arg⁡(w)=π. Then z equal

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Ready to Test Your Skills?

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Let $z$ and $w$ be two non-zero complex numbers such that $| z | = | w |$ and $\arg (z) + \arg (w) = π$ . Then $z$ equal