# 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

 Input Complex number + i Decimal places 0 1 2 3 4 6 8 10 Result Cosine

## 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

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