|{z_1} + {z_2}|, = ,|{z_1}| + |{z_2}| is poss | vedclass

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

Question

(c) $|{z_1} + {z_2}|\, = \,|{z_1}| + |{z_2}|$
$|{z_1} + {z_2}{|^2}\, = \,|{z_1}{|^2} + |{z_2}{|^2} + 2|{z_1}||{z_2}|$
==> $|{z_1}{|^2} + |{z_2}{|

Vedclass · Accepted Answer

$arg\,({z_1}) = arg ({z_2})$

Vedclass · Answer

(c) $|{z_1} + {z_2}|\, = \,|{z_1}| + |{z_2}|$
$|{z_1} + {z_2}{|^2}\, = \,|{z_1}{|^2} + |{z_2}{|^2} + 2|{z_1}||{z_2}|$
==> $|{z_1}{|^2} + |{z_2}{|^2} + 2{\mathop{m Re}
olimits} |{z_1}{\bar z_2}|$
$ = \,|{z_1}{|^2} + |{z_2}{|^2} + 2|{z_1}||{z_2}|$
==> $2{\mathop{m Re}
olimits} |{z_1}{\bar z_2}| = 2|{z_1}||{z_2}|$
==> $2|{z_1}||{\bar z_2}|\cos ({	heta _1} - {	heta _2}) = 2|{z_1}||{z_2}|$
==> $\cos ({	heta _1} - {	heta _2}) = 1$or ${	heta _1} - {	heta _2} = 0$
$arg({z_1}) = arg({z_2})$

$|{z_1} + {z_2}|\, = \,|{z_1}| + |{z_2}|$ is possible if

Similar Questions

If ${z_1}.{z_2}........{z_n} = z,$ then $arg\,{z_1} + arg\,{z_2} + ....$+$arg\,{z_n}$ and $arg$$z$ differ by a

Let ${z_1}$ and ${z_2}$ be two complex numbers with $\alpha $ and $\beta $ as their principal arguments such that $\alpha + \beta > \pi ,$ then principal $arg\,({z_1}\,{z_2})$ is given by

If $z = 3 + 5i,\,\,{\rm{then }}\,{z^3} + \bar z + 198 = $

If $|z - 25i| \le 15$, then $|\max .amp(z) - \min .amp(z)| = $

If $0 < amp{\rm{ (z)}} < \pi {\rm{,}}$then $amp(z)-amp ( - z) = $