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If $z$ is a complex number so that $iz^2-\overline z=0$, then $|z|= ?$

$\begin{array}{1 1}(A) \;0 \;or \;1 \\(B)\;0 \;or\; \large\frac{\sqrt 3}{2} \\(C)\;1\;or \;\large\frac{\sqrt 3}{2} \\(D)\; 0 \;or\;\large\frac{1}{20} \end{array}$

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Let $z=x+iy$
$\overline z=x-iy$
$iz^2-\overline z=0$
If $x=0,\:then\:-y^2+y=0$
If $y=\large-\frac{1}{2}$, then $x^2-\large\frac{1}{4}$$-\large\frac{1}{2}$
$\Rightarrow\:x=\pm\large\frac{\sqrt 3}{2}$
$\therefore\:z=(0,0),\:or\:(0,1),\:or\:(\large\frac{\sqrt 3}{2},-\frac{1}{2}$), $(\large-\frac{\sqrt 3}{2},-\frac{1}{2}$)
answered Jul 17, 2013 by rvidyagovindarajan_1
edited Jul 17, 2013 by rvidyagovindarajan_1

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