How many cube roots does -512 have?

Answer 1

The number -512 has three cube roots in the complex number system. In general, any non-zero complex number has three distinct cube roots. For -512, these roots can be expressed in the form ( r^{1/3} (\cos(\theta/3) + i \sin(\theta/3)) ), where ( r ) is the magnitude and ( \theta ) is the argument of the complex number. The three cube roots are evenly distributed around the unit circle in the complex plane.