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

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Answer 1 · 2015-12-22T03:31:05

Multiply the numerator and denominator by the conjugate of the denominator to find

#(2-i)/(5+i)= 9/26 - 7/26i#

The conjugate of a complex number #a+bi# is #a-bi#. The product of a complex number and its conjugate is a real number. We will use that fact here.

#(2-i)/(5+i) = (2-i)/(5+i)*(5-i)/(5-i)#

#= ((2-i)(5-i))/((5+i)(5-i))#

#= (10 -2i -5i -1)/(25 -5i +5i +1)#

#= (9-7i)/26#

#= 9/26 - 7/26i#