How do you divide #(-5-i)/(-6-9i)#?

1 Answer
Mar 17, 2018

Answer:

#1/3-1/3i#

Explanation:

#"multiply numerator/denominator by the "#
#color(blue)"complex conjugate ""of the denominator"#

#"this ensures the denominator is real"#

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

#"the conjugate of "-6-9i" is "-6color(red)(+)9i#

#rArr((-5-i)(-6+9i))/((-6-9i)(-6+9i))larr"expand using FOIL"#

#=(30-39i-9i^2)/(36-81i^2)#

#=(39-39i)/117=1/3-1/3i#