 A complex number is a number with two totally separate and independent parts, a real part and an imaginary part. You can think of these two parts as representing a point in two-dimensional space. We usually plot the real part on the x-axis and the imaginary part on the y-axis. Just as the everyday numbers like 1, 2 and 3 and so on can represent a one-dimensional quantity like how many apples I need to buy from the supermarket, so complex numbers can represent more complicated ideas that require two dimensions like how current and voltage change over time as they pass through a capacitor. It is sometimes useful to think of complex numbers as a rotation. Multiplying any real vector by the imaginary number i rotates that vector by 90 degrees into the imaginary dimension. If I multiply the vector by i again, it rotates by another 90 degrees. Now it's equal to minus 1. This is why i squared equals minus 1.