IB MATHEMATICS Topic : Complex Numbers – nth Roots of Unity

Finding the 'n roots of unity' means to find all solutions to the equation z^n = 1 (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.