Find six distanct sixth roots of -1 + i root 3 I want check my answer

[r-soy]

Find six distanct sixth roots of -1 + i root 3
I want check my answer



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x = -1 y = root 3



r = 2

tan Q = 2pi/3



-1 + i roo3 = 2 { cos ( 2 pi / 3 ) + i sin 2 pi / 3 )





= 2 e ^2 pi i / 3 }



now six root



-1 + i roo3 = 2^1/6 e ( 2 pi/3 / 6 ) i









now six root

-1 + i root 3 =

 

[Mark44]

Find six distanct sixth roots of -1 + i root 3
I want check my answer



==== >



x = -1 y = root 3



r = 2

tan Q = 2pi/3

Q is 2pi/3, but tan Q is -sqrt(3)/1

-1 + i roo3 = 2 { cos ( 2 pi / 3 ) + i sin 2 pi / 3 )





= 2 e ^2 pi i / 3 }



now six root



-1 + i roo3 = 2^1/6 e ( 2 pi/3 / 6 ) i









now six root

-1 + i root 3 =

You should learn to check your own answers. If you have a complex number z that is one of the 6th roots of -1 + i sqrt(3), then it must be that z⁶ = -1 + i sqrt(3).