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

Solution

Given

$\begin{gathered} \frac{-8i}{4+5i} \\ \\ \Rightarrow\frac{-8\imaginaryI}{4+5\imaginaryI}\times\frac{4-5i}{4-5i}=\frac{-32i-40}{16+25}=-\frac{40}{41}-\frac{32}{41}i \end{gathered}$

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