Geometric Construction of the Square Roots of a Complex Number

This Demonstration shows a geometric construction of the square roots

w

1

and

w

2

of a complex number

z

. The square roots lie on the angle bisector of the argument of

z

and on a circle through the origin of radius

z

, which is the geometric mean of

ON=1

and

z

. The complex number

z

can be selected using the locator.