Q.

If z1, ,z2 , z3 are complex numbers such that z1=z2=z3=1z1+1z2+1z3=1 then z1+z2+z3  is

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a

equal to 1

b

less than 1

c

greater than 3

d

equal to 3

answer is A.

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Detailed Solution

z1=z2=z3=1⇒z1z¯1=z2z¯2=z3z¯3=1∴z1+z2+z3=1z¯1+1z¯2+1z¯3=1z1+1z2+1z3=1
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If z1, ,z2 , z3 are complex numbers such that z1=z2=z3=1z1+1z2+1z3=1 then z1+z2+z3  is