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The complex numbers $z$ satisfying $|z|-4=0$ and $ |z-i|-|z+5i|=0$ are ?

(A) $\pm2\sqrt 3-2i$

(B) $2\sqrt 3\pm 2i$

(C) $2\pm2\sqrt 3$

(D) $\pm2-2\sqrt 3i$

Can you answer this question?

1 Answer

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Given: $|z|-4=0$
$\Rightarrow\:x^2+y^2=16$ where $z=x+iy$
$\Rightarrow\:y=-2$ and
$\Rightarrow\:x=\pm2\sqrt 3$
$\Rightarrow\:z=\pm2\sqrt 3-2i$
answered Jul 27, 2013 by rvidyagovindarajan_1

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