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A complex number is the sum of a real number and an imaginary number, which can be plotted on an Argand Diagram, or complex plane, where the vertical axis is imaginary and the horizontal axis is real.

Complex numbers often give a clean, clear and elegant solution to

problems that are otherwise muddy and convoluted.

Euler gave us the representation that EQN:a+bi=re^{i\theta}, the so-called polar representation of complex numbers.

Complex numbers often give a clean, clear and elegant solution to problems that are otherwise muddy and convoluted.

Examples, explanations and derivations to follow.