If for complex numbers {z_1} and {z_2}, arg({ | vedclass

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

Question

(c) We have $|{z_1} - {z_2}{|^2}$
$ = |{z_1}{|^2} + |{z_2}{|^2} - 2|{z_1}||{z_2}|\cos ({	heta _1} - {	heta _2})$
where ${	heta _1} = arg({z_1})$

Vedclass · Accepted Answer

$||{z_1}| - |{z_2}||$

Vedclass · Answer

(c) We have $|{z_1} - {z_2}{|^2}$
$ = |{z_1}{|^2} + |{z_2}{|^2} - 2|{z_1}||{z_2}|\cos ({	heta _1} - {	heta _2})$
where ${	heta _1} = arg({z_1})$ and ${	heta _2} = arg({z_2})$
Since $arg\,{z_1} - arg\,{z_2} = 0$
$|{z_1} - {z_2}{|^2} = |{z_1}{|^2} + |{z_2}{|^2} - 2|{z_1}||{z_2}|$
$ = {(|{z_1}| - |{z_2}|)^2}$
==> $|{z_1} - {z_2}| = ||{z_1}| - |{z_2}||$

If for complex numbers ${z_1}$ and ${z_2}$, $arg({z_1}/{z_2}) = 0,$ then $|{z_1} - {z_2}|$ is equal to

Similar Questions

If $z$ is a complex number, then $z.\,\overline z = 0$ if and only if

For the complex number $z$, one from $z + \bar z$ and $z\,\bar z$ is

If the conjugate of $(x + iy)(1 - 2i)$ be $1 + i$, then

If $(3 + i)z = (3 - i)\bar z,$then complex number $z$ is

A real value of $x$ will satisfy the equation $\left( {\frac{{3 - 4ix}}{{3 + 4ix}}} \right) = $ $\alpha - i\beta \,(\alpha ,\beta \,{\rm{real),}}$ if