graphic imaginary numbers with vb.net

anyone have experience doing this? when i say imaginary i mean the square root of negative o开发者_运维技巧ne. how would i graph this?

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http://www.wolframalpha.com/input/?i=sqrt(-1)

Or more specifically, http://www.wolframalpha.com/input/?i=plot+sqrt(-1)

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Complex numbers have many applications. They are useful for being able to store two properties (the real and imaginary parts) that behave sensibly when you apply standard math operators on them, like multiplication. Many problems become easy to solve by transforming them to the complex number domain, perform an operation on them that is easy to calculate, then transforming them back.

A good example is calculating the behavior of an electronic circuit that has reactive components. The impedance of a coil in the complex domain is jwL, of a capacitor is 1/jwC (w = omega). Driven with a signal in the complex domain, you can easily calculate the response. In this particular case, graphing the response is meaningful by mapping the real part on the X-axis and the imaginary part on the Y-axis. The length of the vector is the amplitude, the angle is the phase.

The Laplace transform is another complex domain transformation, based on Euler's identity. It has a very useful graphical representation too, plotting the complex roots of the equation within the unity circle allows predicting the stability of a feedback system.

These kind of transforms are popular because they simplify the math or their graphical representation are easy to interpret. Whether yours are equally useful really depends on what the transform does.