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if !z!=3, the area of triangle whose sides are z, wz and z+wz (where w is a complex cube root of unity) is

if !z!=3, the area of triangle whose sides are z, wz and z+wz (where w is a complex cube root of unity) is

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1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 years ago
Ans:
Hello Student,
Please find answer to your question below

|z| = 3
The sides of the triangle are |z|, |wz|, |z+wz|.
|z| = 3
|wz| = |w||z| = 3
|z + wz| = |z(1+w)| = |z||1+w| = 3
So they form an equilateral triangle.
Area:
\frac{\sqrt{3}}{4}|z|^{2}
\frac{9\sqrt{3}}{4}

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