How do you simplify #(2+5i)/ (1-i)#?

1 Answer
sente
Jan 11, 2016

#(2+5i)/(1-i)= -3/2 + 7/2i#

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 produce a real number in the denominator by multiplying the numerator and denominator by the conjugate of the denominator.

#(2+5i)/(1-i) = (2+5i)/(1-i)*(1+i)/(1+i)#

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

# = (-3+7i)/2#

#= -3/2 + 7/2i#

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