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

Question

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

Answer 1

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

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

= (3 + 3i - 2i - 2i²) / (1 - i²)

= (5 + i) / 2

Answer 2

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)

Answer 3

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.