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$z+\overline z=0$ if and only if

(A) $R_e (z)=0$ (B) $I_m (z)=0$ (C) $R_e(z)=I_m(z)$ (D) $R_e(z)=I_m(z)=0$
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  • If $z=x+iy$ then $\overline z=x-iy$
Let $ z=x+iy$
$R_e(z)=x\:\:and\:\:I_m(z)=y$
If $z+\overline z=0$ then
$(x+iy)+(x-iy)=0$
$\Rightarrow\:2x=0$ or $x=0$
$\Rightarrow\:R_e(z)=0$
answered Jul 15, 2013 by rvidyagovindarajan_1
 

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