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a number of the form a+bi where a and b are real numbers and i is the square root of -1

a number of the form a+bi where a and b are real numbers and i is the square root of -1

A number of the form x+iy where i is the squareroot of -1, and x and y are real numbers, known as the"real" and "imaginary" part. Complex numbers can be plottedas points on a two-dimensional plane, known as an Arganddiagram, where x and y are the Cartesian coordinates.An alternative, polar notation, expresses a complex numberas (r e^it) where e is the base of natural logarithms, and rand t are real numbers, known as the magnitude and phase. Thetwo forms are related:r e^it = r cos(t) + i r sin(t) = x + i ywherex = r cos(t)y = r sin(t)All solutions of any polynomial equation can be expressed ascomplex numbers. This is the so-called Fundamental Theoremof Algebra, first proved by Cauchy.Complex numbers are useful in many fields of physics, such aselectromagnetism because they are a useful way of representinga magnitude and phase as a single quantity.