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Let a point z lie on a circle with centre at the origin. If the area of the triangle formed by the points z, 0, and z+ω, where ω is a cube root of unity, is 4√3 square units, then the radius of the circle is:

1. 1 unit
2. 2 units
3. 4 units
4. None of these

Correct answer: None of these

Solution

The area of the triangle formed by the points z, 0, and z+ω can be calculated using the formula for the area of a triangle in the complex plane. Given that the area is 4√3 square units, and knowing that the area of a triangle is also related to the radius of the circumcircle, we can deduce that the radius must be greater than the options provided, leading to the conclusion that 'None of these' is the correct answer.

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