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Let z1 and z2 be nth roots of unity whic...

Let `z_1 and z_2` be nth roots of unity which subtend a right angle at the origin. Then n must be of the form (1) `4k+1` (2) `4k+2` (3) `4k+3` (4) `4k`

Text Solution

Verified by Experts

`Z^n-1=0`
`Z=1^(1/n)`
`Z_1=e^((i2pi)/n)`
`Z_2=e^((i2pi)/n)`
`theta_1=2pik/n`
`theta_2=2pi(k+1)/n`
`theta_2-theta_1=pi/2`
`2pi(k+1)/n-2pi(k)/n=pi/2`
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