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

2 Answers
Mar 15, 2018

Answer:

#(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

Answer:

#=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#