Roots of Complex Numbers

degree n

5

choose root

1

sector opacity

label powers of the chosen root, β n
connect powers of β n with lines
connect powers of β n with spiral
show powers of β n as sectors
emphasize symmetry of roots
emphasize argument of first root

z =

1.4+2.4

Drag the locator, which represents the complex number

z

. The gray dots represent the

n

solutions of the equation

n

β

=z

. As you drag

z

notice these

n

roots are always the vertices of a regular polygon. You can explore the powers of

β

n

for each of the

n

choices of

β

.