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Question

Assertion :Let the fourth roots of unity be z1,z2,z3 and z4, respectively.

z21+z22+z23+z24=0
Reason: z1+z2+z3+z4=0.

A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
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B
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
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C
Assertion is correct but Reason is incorrect
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D
Assertion is incorrect and Reason is correct
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Solution

The correct option is B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
x4=1
x2=±1
x=±1 and x=±i
Hence
z1=1,z2=1,z3=i,z4=i
Thus
z2
=1+111
=0
z
=11+ii
=0
However Statement 2, is not the correct explanation of statement 1.
z21+z22+z23+z24 is 0 since the roots appear in conjugate pairs.

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