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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

Vedclass · Accepted Answer

$-\overline{w}$

Vedclass · Answer

(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:

Similar Questions

The minimum value of $|z-1|+|z-5|$ is

If $z=x+iy$,then the equation $|z+1|=|z-1|$ represents

The locus of the complex number $z$ such that $\arg \left(\frac{z-2}{z+2}\right)=\frac{\pi}{3}$ is:

If $Z$ is a complex number such that $|Z| \leq 3$ and $-\frac{\pi}{2} \leq \operatorname{amp}(Z) \leq \frac{\pi}{2}$,then the area of the region formed by the locus of $Z$ is

The locus of the point $z$ satisfying the equation $|iz - 1| + |z - i| = 2$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module