How do you divide #(-5-3i) -: (7-10i)#?

1 Answer
Jul 6, 2018

Answer:

#(-5-3i)/(7-10i) = -5/149-71/149i#

Explanation:

We can multiply both numerator and denominator by the complex conjugate #7+10i# as follows:

#(-5-3i)/(7-10i) = ((-5-3i)(7+10i))/((7-10i)(7+10i))#

#color(white)((-5-3i)/(7-10i)) = ((-5)(7)+(-5)(10i)+(-3i)(7)+(-3i)(10i))/((7)^2-(10i)^2)#

#color(white)((-5-3i)/(7-10i)) = (-35-50i-21i+30)/(49+100)#

#color(white)((-5-3i)/(7-10i)) = (-5-71i)/149#

#color(white)((-5-3i)/(7-10i)) = -5/149-71/149i#