If |{z_1}|, = ,|{z_2}| and amp,{z_1} + amp,,{ | vedclass

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Question

(b)Let ${z_1} = {r_1}(\cos {	heta _1} + i\sin {	heta _1})$
Then $|{z_1}|\, = \,|{z_2}|\,\, \Rightarrow |{z_2}| = {r_1}$
and $arg({z_1}) + arg({z_2

Vedclass · Accepted Answer

${\bar z_1} = {z_2}$

Vedclass · Answer

(b)Let ${z_1} = {r_1}(\cos {	heta _1} + i\sin {	heta _1})$
Then $|{z_1}|\, = \,|{z_2}|\,\, \Rightarrow |{z_2}| = {r_1}$
and $arg({z_1}) + arg({z_2}) = 0$$&rArr;$  $arg({z_2}) = - arg({z_1}) = - {	heta _1}$
${z_2} = {r_1}[\cos ( - {	heta _1}) - i\sin ( - {	heta _1})] = {r_1}(\cos {	heta _1} - i\sin {	heta _1})$
$ = {\bar z_1}$${\bar z_1} = {z_2}$.

If $|{z_1}|\, = \,|{z_2}|$ and $amp\,{z_1} + amp\,\,{z_2} = 0$, then

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