Let z and w be complex numbers such that over | vedclass

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

Question

(C) Given that $	ext{arg}(zw) = \pi$  $(i)$$\overline{z} + i\overline{w} = 0$ $\Rightarrow \overline{z} = -i\overline{w}$ $\Rightarrow z = i w$ $\Rig

Vedclass · Accepted Answer

$3\pi / 4$

Vedclass · Answer

(C) Given that $	ext{arg}(zw) = \pi$  $(i)$$\overline{z} + i\overline{w} = 0$ $\Rightarrow \overline{z} = -i\overline{w}$ $\Rightarrow z = i w$ $\Rightarrow w = -iz$Substitute $w = -iz$ into $(i)$:$	ext{arg}(z(-iz)) = \pi$$	ext{arg}(-iz^2) = \pi$$	ext{arg}(-i) + 	ext{arg}(z^2) = \pi$$	ext{arg}(-i) + 2	ext{arg}(z) = \pi$Since $	ext{arg}(-i) = -\pi / 2$,we have:$-\pi / 2 + 2	ext{arg}(z) = \pi$$2	ext{arg}(z) = 3\pi / 2$$	ext{arg}(z) = 3\pi / 4$

Let $z$ and $w$ be complex numbers such that $\overline{z} + i\overline{w} = 0$ and $\text{arg}(zw) = \pi$. Then $\text{arg}(z)$ equals

Similar Questions

If $z=1+i \sqrt{3}$ then $|\operatorname{Arg} z|+|\operatorname{Arg} \bar{z}|$ is equal to

Let $z$ and $w$ be two complex numbers such that $\bar{z}+i \bar{w}=0$ and $\operatorname{Arg}(z w)=\pi$. Then,$\operatorname{Arg} z=$

Convert the following into polar form: $\frac{1+3i}{1-2i}$

The amplitude of $\frac{1 + \sqrt{3}i}{\sqrt{3} - i}$ is

Let $z$ be a purely imaginary number such that $\text{Im}(z) > 0$. Then $\text{arg}(z)$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module