Given
[tex]\begin{gathered} z_1=5(\cos15\degree+i\sin15\degree) \\ z_2=3(\cos70\degree+i\sin70\degree) \end{gathered}[/tex]
Find
quotient of the complex numbers and express in trigonometric form.
Explanation
Here , we use
[tex]e^{\pm i\theta}=\cos\theta\pm i\sin\theta[/tex]
so ,
[tex]\begin{gathered} \frac{z_1}{z_2}=\frac{5(\cos15\degree+i\sin15\degree)}{3(\cos70\degree+i\sin70\degree)} \\ \\ \frac{z_1}{z_2}=\frac{5e^{i15\degree}}{3e^{i70\degree}} \\ \\ \frac{z_1}{z_2}=\frac{5}{3}e^{i15\degree-i70\degree} \\ \\ \frac{z_1}{z_2}=\frac{5}{3}e^{i(15\degree-70\degree)} \\ \\ \frac{z_1}{z_2}=\frac{5}{3}e^{-i(55)} \\ \\ \frac{z_1}{z_2}=\frac{5}{3}(\cos55\degree-i\sin55\degree) \\ or \\ \frac{z_1}{z_2}=\frac{5}{3}(\cos305\degree-i\sin305\degree) \\ \end{gathered}[/tex]
Final Answer
Hence , the correct option is
