If z is any non -zero complex number, then area of the triangle formed by the complex numbers z,ωz,z+ωz which represents the sides is
A
√32z2
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B
34|z|
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C
√34∣∣z2∣∣
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D
None of these
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Solution
The correct option is D√34∣∣z2∣∣ Fact:ω=−1+i√32=enπβ and ωz=|z| ...(i)which means \omega is a vector obtained by rotating vector z in anticlockwise direction through an angle 1200 Now |z+ωz|=|z(1+ω)|=∣∣z(−ω2)∣∣=|z|...(ii)⇒z,z+ωz,ωz are sides of equilateral Δ we know that area of equilateral triangle =√34(side)2=√34|z|2