## nth Roots of Unity

Finding the 'n roots of unity' means to find all solutions to the equation (1 being unity).

We can write 1 in complex polar form aswhere Taking the nth root then gives

Fortheare all distinct and can be plotted on an Argand diagram. The roots all lie on a circle of radius 1.

The 5 th roots of unity areforThese areThese solutions are plotted on the Argand diagram below.