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Let z1, z2,z3, be three complex number such that |z1|=|z2|=|z3|=1 and z=(z1+z2+z3)(1/z1+1/z2+1/z3), then |z| can exceed

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Solution: Note that , $1/z_1=arz_1$

$z=(z_1+z_2+z_3)(arz_1+arz_2+arz_3)\ \Rightarrow z=left | z_1+z_2+z_3 ight |^2leq (left | z_1 ight |+left | z_2 ight |+left | z_3 ight |)^2=9$

The maximum value obtained when $z_1=z_2=z_3$

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Deependra Verma

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