Tiny example
A number as a point
The number 3 + 2i means 3 steps across and 2 steps up.
Instead of sitting on a number line, it sits on a plane.
Complex numbers
Numbers with a real part and an imaginary part.
A complex number can be drawn as a point on a plane. That makes it useful for movement, rotation and repeated rules that happen in two directions at once.
Why it matters
Complex numbers make rotation, roots and fractals easier to see. They are the language behind Mandelbrot and Julia sets.
Things to watch for
- Thinking imaginary means fake or useless.
- Forgetting that complex numbers can be represented visually.
- Treating multiplication as only changing size; it can also rotate.
Where it connects
Further MathsArgand diagramsroots of unity