Question

Perform the following division and write the quotient in trigonometric form. Write the magnitude inround it to two decimal places if necessary.- 8i4 + 5i

Answer 1

Given

`\begin{gathered} (-8i)/(4+5i) \\ \\ \Rightarrow(-8\imaginaryI)/(4+5\imaginaryI)*(4-5i)/(4-5i)=(-32i-40)/(16+25)=-(40)/(41)-(32)/(41)i \end{gathered}`

`\begin{gathered} \text{ Let }Z=(-40)/(41)-(32)/(41)i \\ \\ \text{ Magnitude of }Z=|Z|=\sqrt{(-(40)/(41))^2+(-(32)/(41))^2} \\ \\ \Rightarrow|Z|=(8√(41))/(41) \end{gathered}`