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If z1,z2,z3 are any three roots of the e...

If `z_1,z_2,z_3` are any three roots of the equation `z^6=(z+1)^6,` then `arg((z_1-z_3)/(z_2-z_3))` can be equal to

A

`0`

B

`pi`

C

`(pi)/(4)`

D

`-(pi)/(4)`

Text Solution

Verified by Experts

The correct Answer is:
A, B
`(a,b)` Given equation `z^(6)=(z+1)^(6)`
`implies|z^(6)|=|(z+1)^(6)|`
`implies|z|=|z+1|`
`implies` Roots are collinear.
`impliesarg((z_(1)-z_(3))/(z_(2)-z_(3)))=0` or `pi`
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