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Question

If fourth root of unity are z1,z2,z3,z4,, then z21+z22+z23+z24=

A
1
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B
0
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C
i
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D
None of these
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Solution

The correct option is D 0
Square roots of unity are 1 and 1
Fourth roots of unity are as square roots of 1 and 1 i.e., 1,1,i,i
So, we have z1=1,z2=1,z3=i,z4=i
Then, z21+z22+z23+z24=(1)2+(1)2+(i)2+(i)2=1+1+(1)+(1)=22=0

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