A calculus of the absurd

15.2 The Argand diagram

15.2.1 Plotting complex numbers

Complex numbers can be interpreted in a Cartesian fashion110110 Where every point in the plain is uniquely specified by numerical co-ordinates. Instead of an \(x\) and a \(y\) co-ordinate, we can say that we have a real (\(\Re \)) and an imaginary (\(Im\)) co-ordinate.

For example, if we have the expression \(3 + 2\sqrt {-1} = 3 + 2i\), we could say that the co-ordinates are \((3, 2)\), and plot these on a graph.

(-tikz- diagram)

We label the vertical axis as \(\Im \) (or \(\text {Im}\)) - for “imaginary” - and the horizontal axis as \(\Re \) (or \(\text {Re}\)) - for “real”.