Question

Find the quotient of the complex numbers. Express your answer intrigonometric form.

Answer 1

Given

`\begin{gathered} z_1=5(\cos15\degree+i\sin15\degree) \\ z_2=3(\cos70\degree+i\sin70\degree) \end{gathered}`

Find

quotient of the complex numbers and express in trigonometric form.

Step-by-step explanation

Here , we use

`e^(\pm i\theta)=\cos\theta\pm i\sin\theta`

so ,

`\begin{gathered} (z_1)/(z_2)=(5(\cos15\degree+i\sin15\degree))/(3(\cos70\degree+i\sin70\degree)) \\ \\ (z_1)/(z_2)=(5e^(i15\degree))/(3e^(i70\degree)) \\ \\ (z_1)/(z_2)=(5)/(3)e^(i15\degree-i70\degree) \\ \\ (z_1)/(z_2)=(5)/(3)e^(i(15\degree-70\degree)) \\ \\ (z_1)/(z_2)=(5)/(3)e^(-i(55)) \\ \\ (z_1)/(z_2)=(5)/(3)(\cos55\degree-i\sin55\degree) \\ or \\ (z_1)/(z_2)=(5)/(3)(\cos305\degree-i\sin305\degree) \\ \end{gathered}`

Final Answer

Hence , the correct option is