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


a.(1+i)/(2)
b. (1-i)/(2)
c. (5+i)/(2)
d. no solution

3 Answers by Expert Tutors

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Mike C. | Enthusiastic Tutor for Middle and High School StudentsEnthusiastic Tutor for Middle and High S...
4.8 4.8 (82 lesson ratings) (82)
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(3 - 2i) / (1 - i)

= [(3 - 2i)(1 + i)] / (1 - i)( 1 + i)

= (3 + 3i - 2i - 2i2) / (1 - i2)

= (5 + i) / 2

Nataliya D. | Patient and effective tutor for your most difficult subject.Patient and effective tutor for your mos...
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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)

George D. | Statistics/Mathematics TutorStatistics/Mathematics Tutor
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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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