Cube root of a complex function

I need to solve Z^3 = -8-3i, and obtain all cube roots of -8-3i showing that the sum of the cube roots is zero using matlab.

Answer 1

[madhan ravi]

syms Z
ROOTS=solve(Z^3 == -8-3i,Z)
logical(sum(ROOTS)==0)

Answer 2

[James Tursa]

Another way is to simply use the roots( ) function with appropriate polynomial coefficients:

>> roots([1 0 0 (8+3i)])
ans =
   0.8036 + 1.8798i
   1.2261 - 1.6359i
  -2.0297 - 0.2439i