# 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.

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