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For z(1)=""^(6)sqrt((1-i)//(1+isqrt(3)))...

For `z_(1)=""^(6)sqrt((1-i)//(1+isqrt(3))),z_(2)=""^(6)sqrt((1-i)//(sqrt(3)+i))`, `z_(3)= ""^(6)sqrt((1+i) //(sqrt(3)-i))`, prove that `|z_(1)|=|z_(2)|=|z_(3)|`

Text Solution

Verified by Experts

`|z_(1)| = |(1-i)/(1+isqrt(3))|^((1)/(6)) = |(sqrt(2))/(2)| = 2^(-(1)/(12))`
Similary,
`|z_(2)| = 2^((1)/(12)), |z_(3)| = 2^(-(1)/(12))`
Hence, the result.
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