How do you simplify #(10+i)/(4-i)#?

1 Answer
Steve M
Oct 9, 2016

In order to remove the complex denominator, multiply the top and bottom by the complex conjugate of the dominator you want to eliminate, thus:

#(10+i )/(4-i)=(10+i )/(4-i).(4+i)/(4+i)#
# =((10+i )(4+i))/((4-i)(4+i))#

Then multiply out the denominator and the numerator; the denominator will now be real:

#:. (10+i )/(4-i)=((10)(4)+(10)(i)+(4)(i)+(i)(i))/((4)(4)+(4)(-i)+(4)(i)+(i)(-i))#
#=(40+10i+4i+i^2)/(16+4i-4i-i^2)#
#=(40+14i-1)/(16+1)#
#=(39+14i)/(17)#

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