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Let z1,z2,z3 be three vertices of an equilateral triangle circumscribing the circle |z|=12 . If z1=12+i32 and z1,z2,z3 are in anticlockwise sense then z2 is:

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a

1+i3

b

1−i3

c

1

d

−1

answer is D.

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Detailed Solution

z2=z1ei2π/3=12+32icos2π3+isin2π3 =12+32i−12+32i=−34−14=−1

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Let z1,z2,z3 be three vertices of an equilateral triangle circumscribing the circle |z|=12 . If z1=12+i32 and z1,z2,z3 are in anticlockwise sense then z2 is: