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 Assertionx4=1x2=±1x=±1 and x=±iHencez1=1,z2=−1,z3=i,z4=−iThus ∑z2=1+1−1−1=0∑z=1−1+i−i=0However 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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