Complex Numbers 5 Question 15
16. The cube roots of unity when represented on Argand diagram form the vertices of an equilateral triangle.
(1988, 1M)
Analytical & Descriptive Questions
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Answer:
Correct Answer: 16. True
Solution:
- Since, cube root of unity are $1, \omega, \omega^{2}$ given by
$$ \begin{aligned} & A(1,0), B-\frac{1}{2},-\frac{\sqrt{3}}{2}, C-\frac{1}{2},-\frac{\sqrt{3}}{2} \\ & \Rightarrow A B=B C=C A=\sqrt{3} \end{aligned} $$
Hence, cube roots of unity form an equilateral triangle.
