Polar form

Polar form represents a complex number by its magnitude and angle in the complex plane, typically as r(cos θ + i sin θ) or re^{iθ}.

Complex modulus: The nonnegative distance of a complex number from the origin in the complex plane. It supplies the magnitude r in the polar representation.
Complex number: A number expressible as a + bi, where a and b are real numbers and i² = −1. Polar form is one way to represent this broader kind of number.
Complex exponential: An extension of the exponential function to complex inputs, with e^{iθ} = cos θ + i sin θ. Its magnitude-and-phase form is the exponential notation for polar form.
Rectangular form: A complex-number representation a + bi that states its real and imaginary parts directly. It makes addition and subtraction direct, unlike polar form's advantage for products.
Argument of a complex number: An angle describing the direction of a nonzero complex number from the positive real axis. It supplies θ, with values differing by full turns representing the same direction.
Complex plane: A plane in which the horizontal axis represents real parts and the vertical axis represents imaginary parts. It gives geometric meaning to a complex number's distance and direction.
Phasor: A complex number encoding the amplitude and phase of a sinusoidal quantity. Polar form displays a phasor's amplitude and phase directly.
Trigonometric form: A complex-number representation r(cos θ + i sin θ) using magnitude and angle. It is the trigonometric notation for polar form, distinct from exponential notation.
Euler's formula: The identity e^{iθ} = cos θ + i sin θ connecting complex exponentials with trigonometric functions. It gives the exponential form re^{iθ} of the same representation.
Cartesian coordinates: A coordinate system that locates points using perpendicular axes and signed distances along them. The rectangular representation supplies the coordinates converted into polar form.

Linked from 8 pages