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Question

If Z1+Z2+Z3=0 and |Z1|=|Z2|=|Z3|=1, then Z21+Z22+Z23 equals

A
+3
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B
13
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C
1
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D
0
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Solution

The correct option is D 0

As (z1+z2+z3)=0

Therefore, (z1+z2+z3)2=0

z21+z22+z23+2(z1z2+z2z3+z1z3)=0

But,

z1z2+z2z3+z3z1=z1z2z3(1z1+1z2+1z3)

z1z2z3(¯¯¯¯¯z1+¯¯¯¯¯z2+¯¯¯¯¯z3)=0

z21+z22+z23=0


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