![]() ![]() The polar angle for the complex number 0 is indeterminate, but arbitrary choice of the polar angle 0 is common. Hence, the arg function is sometimes considered as multivalued. It can increase by any integer multiple of 2 π and still give the same angle, viewed as subtended by the rays of the positive real axis and from the origin through z. The value of φ is expressed in radians in this article. If the arg value is negative, values in the range (− π, π] or [0, 2 π) can be obtained by adding 2 π. Normally, as given above, the principal value in the interval (− π, π] is chosen. ![]() In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted i, called the imaginary unit and satisfying the equation i 2 = − 1 Re is the real axis, Im is the imaginary axis, and i is the " imaginary unit", that satisfies i 2 = −1. A complex number can be visually represented as a pair of numbers ( a, b) forming a vector on a diagram called an Argand diagram, representing the complex plane. ![]()
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