notes / Integrated Mathematics / chapter 16: Parametric Equations, Polar Coordinates and Complex Numbers
16.3 Basics of Complex Numbers
This page plots complex numbers as points in the plane and starts on the modulus.
The complex plane
Problem 16.3.1. (a) Let ; plot , , and .
(b) For all , how are and related? What about and ?
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(a) , , :
Real and imaginary parts
Problem 16.3.2. (a) Let . Express in terms of .
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Write , so and
Also , so
but that still has in it (as ).
Two further exercises are only started in the notes: one plots and four unlabelled points, and the other is blank.