First slide

Algebra of complex numbers

Question

The number of complex numbers $z$ such that $| z - i | = | z + i | = | z + 1 |$ is

Moderate

A

0
B

1
C

2
D

infinite

Solution

TIP
Note $z$ is circum-centre of the circle passing through three non-collinear points $A (0 + i), B (0 - i)$ and $C (- 1 + 0 i)$
Thus, there is only one value of $z$ .

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