How do you divide #(4+i)/(8+9i)#?

1 Answer
Dec 18, 2016

Answer:

#41/145-28/145i#

Explanation:

To divide the fraction we multiply the numerator/denominator by the #color(blue)"complex conjugate"# of the denominator.

#8+9i" has conjugate " 8-9i#

#rArr(4+i)/(8+9i)=((4+i)(8-9i))/((8+9i)(8-9i))#

expand numerator/denominator using FOIL method.

#=(32-36i+8i-9i^2)/(64-72i+72i-81i^2)#

#color(orange)"Reminder " i^2=(sqrt(-1))^2=-1#

#=(41-28i)/145=41/145-28/145i#