Question

Find the quotient $\frac{z_1}{z_2}$ and express it in rectangular form.

$z_1 = \sqrt{12}(\cos 350\degree + i \sin 350\degree) \text{ and } z_2 = \sqrt{3} (\cos 80\degree + i \sin 80\degree)$

Solution

VerifiedAnswered 2 years ago

Answered 2 years ago

Step 1

1 of 3To find the quotient $\dfrac{z_1}{z_2}$ of given complex numbers use formula $\dfrac{z_1}{z_2}=\dfrac{r_1}{r_2}\left[\cos\left(\theta_1-\theta_2\right)+i\sin\left(\theta_1-\theta_2\right)\right]$.

$\begin{align*} \dfrac{z_1}{z_2}&=\dfrac{\sqrt{12}\left(\cos{350°}+i\sin{350°}\right)}{\sqrt{3}\left(\cos{80°}+i\sin{80°}\right)}\\ \dfrac{z_1}{z_2}&=\dfrac{\sqrt{12}}{\sqrt{3}}\left[\cos\left(350°-80°\right)+i\sin\left(350°-80°\right)\right]\\ \dfrac{z_1}{z_2}&=\sqrt{4}\left(\cos{270°}+i\sin{270°}\right) \end{align*}$

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