Question

Find the quotient of these complex numbers.(8-71) + (4-5) =

Answer 1

Dividing complex numbers formula:

`\begin{gathered} (a+bi)/(c+di)=(a+bi)/(c+di)*(c-di)/(c-di) \\ \\ =(ac+bd)/(c^2+d^2)+(bc-ad)/(c^2+d^2)i \end{gathered}`

For the given division:

`\begin{gathered} (8-7i)/(4-5i)=(8*4+(-7*-5))/(4^2+(-5)^2)+(-7*4-(8*-5))/(4^2+(-5)^2)i \\ \\ =(32+35)/(16+25)+(-28+40)/(16+25)i \\ \\ =(67)/(41)+(12)/(41)i \end{gathered}`Answer: C