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The complex plane


This is a graph with two perpendicular axes, labelled x and y. Any point in the plane can be specified by two numbers, its distance along the x-axis, and its distance along the y-axis, as shown.

Sometimes it is useful to think of the point (a,b) as a complex number a+bi, where i stands for the square root of minus one.

Of course, the square root of minus one does not really exist. We call it an imaginary number. And then we call a the real part of a+bi and b the imaginary part. Some times we use the names real and imaginary axes for the x and y axes respectively.

We can do arithmetic with complex numbers, as long as we remember that i*i = -1

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