How do you divide (2 + i) / ( 5- i ) 2+i5i?

2 Answers
Mar 15, 2018

(9+7i)/269+7i26

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)))2+i5i=(2+i)(5+i)(5i)(5+i)

=(10+5i+2i+i^2)/(25+5i-5i-i^2=10+5i+2i+i225+5i5ii2

Recalling that i^2=-1i2=1

=(9+7i)/26=9+7i26

Mar 15, 2018

=9/26+(7i)/26=926+7i26

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))2+i5i=2+i5i5+i5+i

=(10+5i+2i+i^2)/ (5^2-i^2) =10+5i+2i+i252i2

=(10+7i-1)/(25+1)=10+7i125+1

=(9+7i)/26=9+7i26

=9/26+(7i)/26=926+7i26