How do you simplify #(4+2i)/(3-i)#?

1 Answer
sente
May 28, 2016

Multiply by the conjugate of the denominator to find that
#(4+2i)/(3-i)=1+i#

Explanation:

Given a complex number #a+bi#, the complex conjugate of that number is #a-bi#. A useful property is that the product of a complex number and its conjugate will be a real number. We will use that to eliminate the complex number from the denominator.

#(4+2i)/(3-i) = ((4+2i)(3+i))/((3-i)(3+i))#

#=(10+10i)/10#

#=1+i#

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