First slide

Geometry of complex numbers

Question

If center of a regular hexagon is at the origin and one of the vertices on the Argand diagram is 1 + 2i, then its perimeter is

Moderate

A

$2 \sqrt{5}$
B

$6 \sqrt{2}$
C

$4 \sqrt{5}$
D

$6 \sqrt{5}$

Solution

Let the vertices be z₀, z₁, ..., z₅ w.r.t. center O at origin and $|z_{0}| = \sqrt{5} .$
Now ${ΔOA}_{2} A_{3}$ is equilateral
$\Rightarrow {OA}_{2} = {OA}_{3} = A_{2} A_{3} = \sqrt{5}$
Perimeter $= 6 \sqrt{5}$

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