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

Question

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

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)`

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - 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`

4 views Answered 2023-02-05 15:29