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$|z+\overline z|=|z-\overline z|$ represents ?

(A) A circle passing through origin
(B) A circle having centre origin
(C) A pair of intersecting lines
(D) A pair of parallel lines

1 Answer

Ler $z=x+iy$
$|z+\overline z|=|x+iy+x-iy|=|2x|$
$|z-\overline z|=|x+iy-x+iy|=|2yi|$
$|z+\overline z|=|z-\overline z|$
$\Rightarrow\:x\pm y=0$
which represents a pair of intersecting lines intersecting at origin.
answered Jul 21, 2013 by rvidyagovindarajan_1

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