FACTOID #151: The five countries with the highest coffee consumption are also the five countries whose citizens trust one another the most. Coincidence? Probably.
Rather than represent a point in the plane as a pair of Cartesian coordinates, it can be represented as a single complex number, which can be written at will in either rectangular or polar form.
Complex analytical geometry deals with solving geometrical problems, especially those involving angles, by means of complex algebra. Using Euler's formula,
it is possible to represent any rotation as a complex number.
Complex numbers can therefore be used to advantage to solve problems in elementary geometry. This method is sometimes used in the advanced high-school mathematics, since it allows schoolchildren to write down angle relations in terms of simple formulas.
Complex numbers were first introduced in connection with explicit formulas for the roots of cubic[?] polynomials.
The conjugate of the complex number z corresponds to the transformation which rotates through the same angle as z but in the opposite direction, and scales in the same manner as z; this can be described by the transpose of the matrix corresponding to z.
Complex numbers are used in signal analysis[?] and other fields as a convenient description for periodically varying signals.
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