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Complex numbers consist of a real number plus an imaginary number. If we think of imaginary numbers as having a number line of their own at right angles to the ordinary real number line, then complex numbers exist in a plane called the complex plane. The real and imaginary part are like x and y co-ordinates.

A real number, plus a real multiple of i, where i²=−1.
We use the symbol C for the set { x+iy|x,y ∈ R } .