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