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.

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

\(tan(z) = sinh(0.3+0.5i)\)

\(\displaystyle tan(z) = \frac{sin(2\cdot0.3)}{cos(2\cdot0.3)+cosh(2\cdot 0.5)} + \frac{sinh(2\cdot0.5)}{cos(2\cdot0.3)+cosh(2\cdot 0.5)}i\)

\(\displaystyle tan(z) = \frac{sin(0.6)}{cos(0.6)+cosh(1)} + \frac{sinh(1)}{cos(0.6)+cosh(1)}i\)

\(\displaystyle tan(z) = \frac{0.565}{2.368} + \frac{1.175}{2.368}i\)

\(\displaystyle tan(z) = tan(0.3+0.5i) = 0.238+0.496i\)