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Question

Let z1 and z2 be nth roots of unity which subtend a right angle at the origin, then n must be of the form (where, k is an integer)

A
4k+1
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B
4k+2
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C
4k+3
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D
4k
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Solution

The correct option is D 4k
Since, argz1z2=π2z1z2=cosπ2+i sinπ2=izn1zn2=(i)nin=1n=4k
Alternate Solution

argargz2z1=π2z2z1=z2z1eiπ2z2z1=i(z2z1)n=in
z1 and z2 are nth roots of unity.
zn1=zn2=1(z2z1)n=1in=1n=4k, where k is an integer.

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