Question
Let $z_{1}=r_{1}\left(\cos \theta_{1}+i \sin \theta_{1}\right)$ and $z_{2}=r_{2}\left(\cos \theta_{2}+i \sin \theta_{2}\right) $be two complex numbers. Then $z_{1} z_{2}=$ _________________ $[\cos ($ __________________ $+i \sin$ ________________.
Step 1
The magnitude of a complex number in polar form is given by the coefficient of the trigonometric part. So, we multiply $r_{1}$ and $r_{2}$ to get the magnitude of the product. Show more…
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Given two complex numbers $z_{1}=r_{1}\left(\cos \theta_{1}+i \sin \theta_{1}\right)$ and $z_{2}=r_{2}\left(\cos \theta_{2}+i \sin \theta_{2}\right), z_{2} \neq 0,$ show that $$ \frac{z_{1}}{z_{2}}=\frac{r_{1}}{r_{2}}\left[\cos \left(\theta_{1}-\theta_{2}\right)+i \sin \left(\theta_{1}-\theta_{2}\right)\right] $$
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