cosh2z +sinh2z =cosh2z
You asked:
Solve the equation \(\cosh\left( 2 z \right) + \sinh\left( 2 z \right) = \cosh\left( 2 z \right)\) for the variable \(z\).
MathBot Answer:
The real solution is: \[z = 0\]
The complex solutions are: \[\begin{aligned}z &= \left\{\pi i n\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{3.1415927 n i\; \middle|\; n \in \mathbb{Z}\right\}\\z &= \left\{\frac{i \left(\pi + 2 \pi n\right)}{2}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{0.5 i \left(6.2831853 n + 3.1415927\right)\; \middle|\; n \in \mathbb{Z}\right\}\end{aligned}\]
\(i\) is the imaginary unit, defined as \(i^2 = -1\).