SOLUTION: Use De Moivre’s Theorem to solve for z and leave the answer in polar form with the angle in radians z^3 = −8

Your equation is

    z^3 = -8,             (1)

or, in polar form

    z^3 = .     (2)


According to the DeMoivre's theorem, the solutions are these three complex numbers in polar form


    a)   = 


    b)   =  = 


    c)   =  = 


The modulus is the cube root of 8, i.e. 2.


The argument of the first root is    of the argument of the right side equation (2).


The arguments of the second and third root have consecutive increments of   from the argument of the first root.


Also notice that the complex root (b) is in reality the REAL number -2.