Let ${z_1},{z_2},{z_3}$ be three vertices of an equilateral triangle circumscribing the circle $\left| z \right| = \frac{1}{2}.$ If ${z_1} = \frac{1}{2} + i\frac{{\sqrt 3 }}{2}$ and ${z_1},{z_2},{z_3}$ were in anticlockwise sense, then ${z_2}$ is

JEE MATHEMATICS MCQ: COMPLEX NUMBERS

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Let

{z_1},{z_2},{z_3}

be three vertices of an equilateral triangle circumscribing the circle

\left| z \right| = \frac{1}{2}.

{z_1} = \frac{1}{2} + i\frac{{\sqrt 3 }}{2}

and

{z_1},{z_2},{z_3}

were in anticlockwise sense, then

{z_2}

View answer and explanation

Correct option: D

- 1

The correct answer is D (

- 1

) because, in an equilateral triangle, the vertices are equally spaced around the circumscribing circle, and using the properties of complex numbers, z2 = -1.

JEE MATHEMATICS MCQ: COMPLEX NUMBERS

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