I have to remember to convert -4√3 – 4i) in to polar form
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
I have to remember to convert -4√3 – 4i) in to polar form
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
z = 8 cis (2πk-5π/6) for k = 1,2,3.
z^{1/3} = 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)
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.