How do you simplify #(2+ i)/(1-i)# completely?

1 Answer
sente
Dec 25, 2015

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

#(2+i)/(1-i)= 1/2 + 3/2i#

Explanation:

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 this fact to eliminate the complex number from the denominator of the given expression.

#(2+i)/(1-i) = ((2+i)(1+i))/((1-i)(1+i))#

#= (2 + 2i + i - 1)/(1 + i - i + 1)#

#= (1+3i)/2#

#= 1/2 + 3/2i#

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