Question

Perform the following division and write the quotient in trigonometric form. Write the magnitude in exact form. Write the argument in radians and round it to twodecimal places if necessary.-3 - 6i6 + 4i

Answer 1

To perform the division of complex numbers, we have to multiply by the unitary conjugate of the denominator. In this case we would have the following:

$\begin{gathered} \frac{-3-6i}{6+4i}*\frac{6-4i}{6+4i}=\frac{(-3-6i)(6-4i)}{(6)²-(4i)²}=\frac{-18+12i-36i+24i²}{36-16i²} \\ =\frac{-42-24i}{52} \end{gathered}$

therefore, the result of the division is -42/52 -24/52i