Let z₁ = 6 + i and z₂ = 4 -3i . Let z be a complex number such that arg left( {frac{{z - {z

English

Gujarati

Hindi

4-1.Complex numbers

normal

Let $z_1 = 6 + i$ and $z_2 = 4 -3i$. Let $z$ be a complex number such that $arg\ \left( {\frac{{z - {z_1}}}{{{z_2} - z}}} \right) = \frac{\pi }{2}$, then $z$ satisfies -

A

$|z -(5 -i)| = 5$

B

$|z -(5 -i)| = \sqrt 5 $

C

$|z -(5 + i)| = 5$

D

$|z -(5 + i)| = \sqrt 5 $

Solution

$C=\frac{Z_{1}+Z_{2}}{2}$

$r=\frac{\left|z_{1}-z_{2}\right|}{2}$

Standard 11

Mathematics

Share

Similar Questions

Let $\bar{z}$ denote the complex conjugate of a complex number $z$ and let $i=\sqrt{-1}$. In the set of complex numbers, the number of distinct roots of the equation

$\bar{z}-z^2=i\left(\bar{z}+z^2\right)$ is. . . . . .

normal

(IIT-2022)

Argument and modulus of $\frac{{1 + i}}{{1 – i}}$ are respectively

easy

Let $\alpha=8-14 i , A=\left\{ z \in C : \frac{\alpha z -\bar{\alpha} \overline{ z }}{ z ^2-(\overline{ z })^2-112 i }=1\right\}$ and $B =\{ z \in C 😐 z +3 i |=4\}$ Then $\sum_{z \in A \cap B}(\operatorname{Re} z-\operatorname{Im} z)$ is equal to $……………$.

hard

(JEE MAIN-2023)

Which of the following are correct for any two complex numbers ${z_1}$ and ${z_2}$

normal

If ${z_1},{z_2}$ are two complex numbers such that $\left| {\frac{{{z_1} – {z_2}}}{{{z_1} + {z_2}}}} \right| = 1$ and $i{z_1} = k{z_2}$, where $k \in R$, then the angle between ${z_1} – {z_2}$ and ${z_1} + {z_2}$ is

hard