First slide

Geometry of complex numbers

Question

The inequality $| z - i | < | z + i |$ represents the region

Moderate

A

$Re (z) > 0$
B

$Re (z) < 0$
C

$Im (z) > 0$
D

$Im (z) < 0$

Solution

$| z - i | = | z + i |$ represents the real axis.
As $z = i satisfies | z - i | < | z + i |$ , we get
$| z - i | < | z + i |$ represent $Im (z) > 0$

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