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WOLFRAM|DEMONSTRATIONS PROJECT

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
.
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