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simplify (3-2i)/(1-i)

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3 Answers

i = √(-1)  ---> i2 = - 1 
(a + b)(a - b) = a2 - b2 
~~~~~~~~~~
  3 – 2i
———— =
  1 – i

 (3 – 2i)(1 + i)
——————— =
 (1 – i)(1 + i)

 3 – 2i + 3i – 2i2 
———————— =
     12 – i 2 

  5 + i 
————
    2 

The answer is (c)

In order to simplify complex number fractions, multiply the numerator and denominator by the denominator's complex conjugate.  In this case, the complex conjugate of (1-i) is (1+i).  This will give you a real number in the denominator, and you should be able to figure out the numerator. Let me know if you need any further help.

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