Roots

This shows all n-th roots (red) of a complex number (black)

     z =a + bi = r  [ cos f  +  i sin f ]

in the complex plane. They are of the form

     u_i  =   r^1/n  [ cos (f/n + k 360/n)  +  i sin (f/n  + k 360/n) ]

where k = 0, 1, 2, ..., n-1.

Click and/or drag for a new position of z.