3.9.6—Complex numbers

Represent z=a+bi by the point (a,b). Addition is vector addition, modulus is distance from the origin and conjugation reflects the point in the real axis.

Use geometry to check algebraic results: conjugates have the same modulus, and z+w is the diagonal endpoint of the parallelogram formed by z and w.

The points 1+i and 1−i are reflections with modulus √2; their sum is the real point 2.

The Argand-plane coordinates are not a graph of y=f(x); the imaginary axis is a second coordinate, not an output scale.