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# Number of solutions of the equation $\;z^{2}+|z|^{2} =0\;$ is

$(a)\;1\qquad(b)\;2\qquad(c)\;3\qquad(d)\;infinitely\;many$

Can you answer this question?

Answer : $\;infinitely \;many$
Explanation :
$\;z^{2}+|z|^{2} =0\; ,z \neq 0$
$x^{2}-y^{2} + 2 i xy +x^{2} +y^{2}=0$
$2x^{2} +i2xy=0\;$ => $\;2x(x+iy)=0$
$x=0 \; or\; x+iy=0\;$ not possible
Therefore , $x=0 \;, z \neq 0$
So y can have any real value.Hence infinitely many solutions .
answered Apr 19, 2014 by