Q.

Let z1,z2,z3  be three complex numbers such that z1=z2=z3=1 and z=z1+z2+z31z1+1z2+1z3, than |z| cannot exceed

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a

1

b

3

c

6

d

9

answer is D.

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Detailed Solution

Note that 1z1=z¯1etc. thusz=z1+z2+z3z¯1+z¯2+z¯3=z1+z2+z32≤z1+z2+z32=9The maximum value is obtained when z1=z2=z3=1
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Let z1,z2,z3  be three complex numbers such that z1=z2=z3=1 and z=z1+z2+z31z1+1z2+1z3, than |z| cannot exceed