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Find the quotient z1z2\frac{z_1}{z_2} and express it in rectangular form.

z1=4(cos280°+isin280°) and z2=4(cos55°+isin55°)z_1 = 4(\cos 280\degree + i \sin 280\degree) \text{ and } z_2 = 4(\cos 55\degree + i \sin 55\degree)

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To find the quotient z1z2\dfrac{z_1}{z_2} of given complex numbers use formula z1z2=r1r2[cos(θ1θ2)+isin(θ1θ2)]\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].

z1z2=4(cos280°+isin280°)4(cos55°+isin55°)z1z2=44[cos(280°55°)+isin(280°55°)]z1z2=(cos225°+isin225°)\begin{align*} \dfrac{z_1}{z_2}&=\dfrac{4\left(\cos{280°}+i\sin{280°}\right)}{4\left(\cos{55°}+i\sin{55°}\right)}\\ \dfrac{z_1}{z_2}&=\dfrac{4}{4}\left[\cos\left(280°-55°\right)+i\sin\left(280°-55°\right)\right]\\ \dfrac{z_1}{z_2}&=\left(\cos{225°}+i\sin{225°}\right) \end{align*}

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