Home Maths Complex Number Skill Builder Let be the vertices of an equilateral tri-a…
Maths Complex Number Skill Builder Single Correct MCQ
Published on: August 14, 2026

Let be the vertices of an equilateral tri-angle in the Argand plane, then the number , is

A
purely real
B
purely imaginary
C
a complex number with non-zero real and imaginary parts
D
none of these

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Text Solution

Verified by Experts
The correct answer is:
B

Step 1: Use equilateral triangle rotation

In an equilateral triangle, rotating one side by gives another side:

Step 2: Rewrite the expression

Substitute :

Step 3: Check the nature

has zero real part after simplification, so it is purely imaginary.

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