Let z and w be two non-zero complex numbers s | vedclass

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(D) Let $z = r(\cos 	heta_1 + i \sin 	heta_1)$ and $w = r(\cos 	heta_2 + i \sin 	heta_2)$,where $|z| = |w| = r$.Given $arg(z) + arg(w) = 	heta_1

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$-\overline{w}$

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(D) Let $z = r(\cos 	heta_1 + i \sin 	heta_1)$ and $w = r(\cos 	heta_2 + i \sin 	heta_2)$,where $|z| = |w| = r$.Given $arg(z) + arg(w) = 	heta_1 + 	heta_2 = \pi$,so $	heta_1 = \pi - 	heta_2$.Substituting this into $z$:$z = r(\cos(\pi - 	heta_2) + i \sin(\pi - 	heta_2))$$z = r(-\cos 	heta_2 + i \sin 	heta_2)$Since $\overline{w} = r(\cos 	heta_2 - i \sin 	heta_2)$,we have $-\overline{w} = r(-\cos 	heta_2 + i \sin 	heta_2)$.Thus,$z = -\overline{w}$.

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

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