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What are the values of all the cube roots (Z = -4v3 - 4i)?

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2 Answers

r =(((-4)(3)^(1/2))^2  + ((-4)^2))^(1/2) = 8

θ = arctan (-4/(-4(3)^(1/2) = 7∏/6.

roots = 2 (cos (7∏/18 + 12n∏/18) = i sin(7∏/18 + 12n∏/18), n = 0, 1, 2

Comments

roots = 2 (cos (7?/18 + 12n?/18)  +  i sin(7?/18 + 12n?/18), n = 0, 1, 2

 

I didn't hit <Shift> when pressing the  (+) sign and got (=).  Right button, wrong function.

z = 8 cis (2πk-5π/6) for k = 1,2,3.

z1/3 = 2 cis (2πk/3 - 5π/18) for k = 1,2,3.

      = 2 cos(π/18) + 2i sin(π/18)

       or 2 cos(7π/18) + 2i sin(7π/18)

       or 2 cos(13π/18) + 2i sin(13π/18)