# Imaginary number

There is no real number which squares to give $-1$. However, we can define an object which squares to $-1$. This is traditionally called $i$ in mathematics and $j$ in physics and engineering (to avoid confusion with $i$ meaning an electrical current), so $i^2=-1$. Thus we find that

• the square roots of $-1$ are $i$ and $-i$
• the square roots of $-4$ are $2i$ and $-2i$

and so on.

We call real multiples of $i$ (that is, $ai$ for some real number $a$) imaginary numbers.

We can visualise imaginary numbers as lying along a number line like the ordinary real number line, but at right angles to it. These two number lines together form a plane called the complex plane.