For n N , a complex number is called an n -th root of unity if ^n=1 . Then

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1. Athe product of all the distinct n -th roots of unity is (-1)^n .
2. B_ j=0 ^4 |z₁+ ^ 2 j z₂ |^2=5 ( |z₁ |^2+ |z₂ |^2 ) for any z₁, z₂ C .
3. Cif n 5 and is an n -th root of unity different from 1 then _ j=0 ^ n-1 |z₁+ ^j z₂ |^2=n ( |z₁ |^2+ |z₂ |^2 ) f
4. Dif n 5 then the complex conjugate of an n -th roots of unity is an n -th root of unity.