$z$ and $w$ are two non zero complex no.s such that $|z|=|w|$ and $\operatorname{Arg} z+\operatorname{Arg} w=\pi$ then $z$ equals

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Aicharya · Accepted Answer

Let $|\mathrm{z}|=|\omega|=\mathrm{r} \quad 	herefore \mathrm{z}=\mathrm{re}^{\mathrm{i} 	heta}, \omega=\mathrm{re}^{\mathrm{i} \phi}$ where $	heta+\phi=\pi \quad 	herefore \bar{\omega}=\mathrm{re}^{-\mathrm{i \phi}}$ $	herefore z=\mathrm{re}^{i(\pi-\phi)}=\mathrm{re}^{\mathrm{i} \pi} \cdot \mathrm{e}^{-i \phi}=-\mathrm{re}^{-i \phi}=-\bar{\omega}$

$z$ and $w$ are two non zero complex no.s such that $|z|=|w|$ and $\operatorname{Arg} z+\operatorname{Arg}…

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