First slide

Geometry of complex numbers

Question

The points in the set ${Z \in C : A r g (\frac{z - 4}{z - 12 i}) = \frac{π}{2}}$ lie on the curve which is a

Easy

A

Circle
B

Pair of lines
C

Parabola
D

Hyperbola

Solution

$A r g [\frac{(x - 4) + i y}{x + i (y - 12)}] = \frac{π}{2} \Rightarrow x (x - 4) + y (y - 12) = 0$

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