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Prove that, $\tan Z = aZ$ where $a>0$ and $a \in \mathbb{R}$ has infinitely many roots.

I know how to solve if $Z \in \mathbb{R}$. I will draw the graphs and will find where the graphs cut. But how to solve them in complex ? Will anybody please help?

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    If you know that there are infinitely many real solutions, what stops you from concluding that there are infinitely many complex solutions? – 2017-01-21
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    You cant evaluate the zeros without the use of approximations. I think you just must prove that they are infinite solutions. – 2017-01-21

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