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Equation of Circle in Complex Form

If |z|=r. A...

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If $| z | = r$ . Area of the triangle whose vertices are $z, ω z$ and $z + ω z$ , where $ω$ is the non real cube root of unity, is $4 \sqrt{3}$ sq. units, then the value of $r$ is

A

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B

2

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C

3

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D

n o n e o f t h e s e

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z

lies on the circle centered at origin. lf area of the triangle whose vertices are

z

ω z

z + ω z

ω

is the cube root of unity, is

4 \sqrt{3}

The radius of the circle is?

ω z

z + ω z

represent three vertices of

Δ A B C

ω

is cube root unity, then

| z_{1} | = | z_{2} | = | z_{3} | = 1

z_{1} + z_{2} + z_{3} = 0

, then area of the triangle whose vertices are

z_{1}, z_{2}, z_{3}

| z - 1 | \leq 2

∣ ∣ ω z - 1 - ω^{2} ∣ ∣ = a

ω

is a cube root of unity), then complete set of values of

a

ω

ω^{2}

ω

is a non-real cube root of unity) are two vertices of an equilateral triangle in the Argand plane, then the third vertex

z

may be represented by

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