Tangent of a complex number
Calculator for the tangent of a complex number
This function returns the tangent to an angle specified as a complex number.
To perform the calculation, enter the complex number. Then click on the 'Calculate' button.
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Formulas for tangent of complex number
In the following description, \(z\) stands for the complex number. \(x\) stands for the real value \(Re\) and \(y\) for the imaginary value \(Im\).
\(\displaystyle tan(z) = \frac{sin(2x)}{cos(2x)+cosh(2y)} + \frac{sinh(2y)}{cos(2x)+cosh(2y)}i\)
Example
\(tan(z) = sinh(0.3+0.5i)\)
\(\displaystyle tan(z) = \frac{sin(2\cdot0.3)}{cos(2\cdot0.3)+cosh(2\cdot 0.5)} + \frac{sinh(2\cdot0.5)}{cos(2\cdot0.3)+cosh(2\cdot 0.5)}i\)
\(\displaystyle tan(z) = \frac{sin(0.6)}{cos(0.6)+cosh(1)} + \frac{sinh(1)}{cos(0.6)+cosh(1)}i\)
\(\displaystyle tan(z) = \frac{0.565}{2.368} + \frac{1.175}{2.368}i\)
\(\displaystyle tan(z) = tan(0.3+0.5i) = 0.238+0.496i\)
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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