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4-1.Complex numbers
normal
જો $|{z_1}|\, = \,|{z_2}|$ અને $amp\,{z_1} + amp\,\,{z_2} = 0$, તો
A
${z_1} = {z_2}$
B
${\bar z_1} = {z_2}$
C
${z_1} + {z_2} = 0$
D
${\bar z_1} = {\bar z_2}$
Solution
(b)Let ${z_1} = {r_1}(\cos {\theta _1} + i\sin {\theta _1})$
Then $|{z_1}|\, = \,|{z_2}|\,\, \Rightarrow |{z_2}| = {r_1}$
and $arg({z_1}) + arg({z_2}) = 0$$⇒$ $arg({z_2}) = – arg({z_1}) = – {\theta _1}$
${z_2} = {r_1}[\cos ( – {\theta _1}) – i\sin ( – {\theta _1})] = {r_1}(\cos {\theta _1} – i\sin {\theta _1})$
$ = {\bar z_1}$${\bar z_1} = {z_2}$.
Standard 11
Mathematics
