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Question Number 93827 by oustmuchiya@gmail.com last updated on 15/May/20

$$simplify:\frac{{(cos\alpha +\mathbf{i}sin\alpha )}^3}{{(sin\beta +\mathbf{i}cos\beta )}^4}$$

Commented by PRITHWISH SEN 2 last updated on 15/May/20

$$\frac{{\mathrm{e}}^{\mathbf{i}3\mathit{\alpha }}}{{\mathrm{e}}^{\mathbf{i}4(\frac{\pi }{2}-\beta )}}={\mathbf{e}}^{\mathbf{i}(3\mathit{\alpha }+4\mathit{\beta })}=\mathbf{cos}(3\mathit{\alpha }+4\mathit{\beta })+\mathbf{isin}(3\mathit{\alpha }+4\mathit{\beta })$$

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