Give an example of unbounded and entire function on $\mathbb{C}$ such that its restriction on $\mathbb{R}$ is real valued bounded function. Justify

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Give an example of unbounded and entire function on $\mathbb{C}$ such that its restriction on $\mathbb{R}$ is real valued bounded function. Justify

I don't have any idia of such example. Please help with justification.

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Hint: Trigonometric functions.