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Question

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
34z2
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D
None of these
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Solution

The correct option is D 34z2
Fact: ω =1+i32=enπβ and ω z=|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

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