# arrow_back Let $z_{1}=\left|z_{1}\right|\left(\cos \left(\theta_{1}\right)+i \sin \left(\theta_{1}\right)\right)$ and $z_{2}=\left|z_{2}\right|\left(\cos \left(\theta_{2}\right)+i \sin \left(\theta_{2}\right)\right)$ be two complex numbers.

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Let $z_{1}=\left|z_{1}\right|\left(\cos \left(\theta_{1}\right)+i \sin \left(\theta_{1}\right)\right)$ and $z_{2}=\left|z_{2}\right|\left(\cos \left(\theta_{2}\right)+i \sin \left(\theta_{2}\right)\right)$ be two complex numbers. Prove that $z_{1} z_{2}=\left|z_{1} \| z_{2}\right|\left(\cos \left(\theta_{1}+\theta_{2}\right)+i \sin \left(\theta_{1}+\theta_{2}\right)\right)$ and $\frac{z_{1}}{z_{2}}=\frac{\mid z_{1}|}{\left|z_{2}\right|}\left(\cos \left(\theta_{1}-\theta_{2}\right)+i \sin \left(\theta_{1}-\theta_{2}\right)\right) .$

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