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Question Number 19687 by Tinkutara last updated on 14/Aug/17

Let z_{1}, z_{2}, z_{3} be three vertices of an

equilateral triangle circumscribing the

circle ∣ z ∣ = \frac{1}{2} . If z_{1} = \frac{1}{2} + \frac{\sqrt{3} i}{2} and z_{1},

z_{2}, z_{3} are in anticlockwise sense then z_{2} is

Answered by ajfour last updated on 14/Aug/17

z_{2} = z_{1} e^{i 2 π / 3} = e^{i π / 3} . e^{i 2 π / 3} = e^{i π} = - 1 .

Commented by Tinkutara last updated on 14/Aug/17

Thank you very much Sir!