First slide

Geometry of complex numbers

Question

Which of the following equations can represent a triangle:

Easy

A

$| z - 1 | = | z - 2 |$
B

$| z - 1 | = | z - 2 | = | z - i |$
C

$| z - 1 | - | z - 2 | = 2 a$
D

${| z - 1 |}^{2} + {| z - 2 |}^{2} = 4$

Solution

          $| z - 1 | = | z - 2 | = | z - i |$
(i)       $| z - 1 | = | z - i |$
Represents a straight line through origin i.e., $y = x$
(ii)          $| z - 1 | = | z - 2 | \Rightarrow x = \frac{3}{2}$
which is a straight line
(iii)         $| z - 2 | = | z - i | \Rightarrow 4 x - 2 y = 3$
which is a straight line

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