Angle of complex number
Calculator for the angle of a complex number
This calculator calculates the angle of a complex number. For calculation enter a complex number, then click the 'Calculate' button.
The result is the angle to the x-axis, it can be displayed in degrees or radians.
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Angle φ = 45°
Description of the angle of a complex number
Every complex number \(z\) can be represented as a vector in the Gaussian number plane. This vector is uniquely defined by the real part and the imaginary part of the complex number \(z\).
A vector emanating from the zero point can also be used as a pointer. This pointer is uniquely defined by its length and the angle \(φ\) to the real axis (x).
Positive angles are measured counterclockwise, negative angles are clockwise.
Formula and example
\(\displaystyle θ = tan^{-1}\left(\frac{y}{x}\right) \)
\(\displaystyle θ = tan^{-1}\left(\frac{3}{4}\right) ≈ 36.87 \)
More complex functions
Absolute value (abs) • Angle • Conjugate • Division • Exponent • Logarithm to base 10 • Multiplication • Natural logarithm • Polarform • Power • Root • Reciprocal • Square root •Cosh • Sinh • Tanh •
Acos • Asin • Atan • Cos • Sin • Tan •
Airy function • Derivative Airy function •
Bessel-I • Bessel-Ie • Bessel-J • Bessel-Je • Bessel-K • Bessel-Ke • Bessel-Y • Bessel-Ye •
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