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Zeroes of trigonometric-like function

Consider a function $f(z)=\cos(z)\cosh(az)+\sin(z)\sinh(bz)$ for $z\in \mathbb{C}, a,b \in \mathbb{R}$. Denote $D\subseteq \mathbb{R}^2$ being the set of such pairs $(a,b)$ of parameters so that NOT A …
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