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\text { Let } z_{1}=r_{1}\left(\cos \theta_{1}+i \sin \theta_{1}\right) \text { and } z_{2}=r_{2}\left(\cos \theta_{2}+i \sin \theta_{2}\right) \text { be complex numbers, where } r_{1}, r_{2}, \theta_{1}, \theta_{2} \in \mathbb{R} \text {. Prove, using standard trigonometric identities, that } \frac{z_{1}}{z_{2}}=\frac{r_{1}}{r_{2}}\left(\cos \left(\theta_{1}-\theta_{2}\right)+i \sin \left(\theta_{1}-\theta_{2}\right)\right) \text {. } Use this result to calculate \frac{1+i \sqrt{3}}{1-i} leaving your result in polar form.

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