How do you divide (2 + i) / ( 5- i ) ?

2 Answers
Mar 15, 2018

(9+7i)/26

Explanation:

Dividing complex numbers is similar to rationalizing the denominator of a surd.

(2+i)/(5-i)=((2+i)color(green)((5+i)))/((5-i)color(green)((5+i)))

=(10+5i+2i+i^2)/(25+5i-5i-i^2

Recalling that i^2=-1

=(9+7i)/26

Mar 15, 2018

=9/26+(7i)/26

Explanation:

If you multiply a given fraction by 1 you do not change it.
Also, if a fraction has the same numerator and denominator it equals 1.
Now lets apply the following trick:

(2+i)/(5-i)=(2+i)/(5-i)*color(red)((5+i)/(5+i))

=(10+5i+2i+i^2)/ (5^2-i^2)

=(10+7i-1)/(25+1)

=(9+7i)/26

=9/26+(7i)/26