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Question

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

A
Equal to 1
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B
Less than 1
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C
Greater than 3
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D
Equal to 3
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Solution

The correct option is A Equal to 1
1=1z1+1z2+1z3=z1¯z1z1+z2¯z2z2+z3¯z3z3
[|¯z12=1=z1¯z1]
=|¯z1+¯z2+¯z3|=|¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯z1+z2+z3|=|z1+z2+z3|
[|¯z1|=|z1|]

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