27Oct/160

## Square Root of a Complex Number using Compass and Straight Edge Geometry

Also available as an interactive applet (scrollwheel or pinch to zoom so you can adjust the axis how you want).

Descartes allowed a line segment of unit length to find roots. The rest of the construction is completed with just Euclid's compass and straight edge.

Given: a complex number C plotted on the complex plane.

Bisect the angle formed between C, the origin O, and the positive X (real) axis.

Extend OC past O by a unit line segment to U.

Find the midpoint, M, between U and C.

Construct a half-circle centered at M through U and C.

Draw the perpendicular to UC through O to intersect the half-circle at I.

Draw a circle centered at O through I.

The circle intersects the bisector at S.

S is a square root of C.

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