Q.

If |z1|=|z2|=...........|zn|=1, then the value of |z1+z2+.......zn|-|1z1+1z 2+......+1zn|  is

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a

0

b

1

c

–1

d

None

answer is A.

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Detailed Solution

Given that |z1|=|z2|=...........|zn|=1, ⇒z1z1¯=z2z2¯=............=znzn¯=1 ⇒z1¯=1z1,z2¯=1z2,z3¯=1z3,............zn¯=1zn ∴|z1+z2+z3+.........+zn|−|1z1+1z2+1z3,............+1zn| =|z1+z2+z3+.........+zn|−|z1¯+z2¯+......+zn¯|=0
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Get ₹ 1 crore* worth scholarship for JEE / NEET / Foundation
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