z^3 = -4i
(r (cos(t) + i sin(t)) )^3 = r^3 [cos(3t) + i sin(3t)] = -4 i = 4 [ 0 - i ]
So r^3 = 4, cos(3t) = 0, sin(3t) = -1
So r = 4^(1/3), 3t = 3pi/2, so t = pi/2
So z = 4^(1/3) e^[ i pi/2 ]
{x= + 1.5874 i },
{x = -1.37473 - 0.793701 i},
{x -> 1.37473 - 0.793701 i }
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Verified answer
z^3 = -4i
(r (cos(t) + i sin(t)) )^3 = r^3 [cos(3t) + i sin(3t)] = -4 i = 4 [ 0 - i ]
So r^3 = 4, cos(3t) = 0, sin(3t) = -1
So r = 4^(1/3), 3t = 3pi/2, so t = pi/2
So z = 4^(1/3) e^[ i pi/2 ]
{x= + 1.5874 i },
{x = -1.37473 - 0.793701 i},
{x -> 1.37473 - 0.793701 i }