Tangent of a complex number

Calculator for the tangent of a complex number

Tangent calculator

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.

Complex number tangent calculator

Complex number +  i
Decimal places

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 \(Im\).

\(\displaystyle tan(z) = \frac{sin(2x)}{cos(2x)+cosh(2y)} + \frac{sinh(2y)}{cos(2x)+cosh(2y)}i\)


\(tan(z) = sinh(0.3+0.5i)\)
\(\displaystyle tan(z) = \frac{sin(2\cdot0.3)}{cos(2\cdot0.3)+cosh(2\cdot 0.5)} + \frac{sinh(2\cdot0.5)}{cos(2\cdot0.3)+cosh(2\cdot 0.5)}i\)
\(\displaystyle tan(z) = \frac{sin(0.6)}{cos(0.6)+cosh(1)} + \frac{sinh(1)}{cos(0.6)+cosh(1)}i\)
\(\displaystyle tan(z) = \frac{0.565}{2.368} + \frac{1.175}{2.368}i\)
\(\displaystyle tan(z) = tan(0.3+0.5i) = 0.238+0.496i\)
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