Simplify the expression: (3 + 2i) / (1 - i), where 'i' is the imaginary unit (i² = -1)

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

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

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

= (3+(-2)+5i)/2

= (1+5i)/2

 

(1+5i)/2 or 1/2+5/2i

Here is how you can calculate it:

 

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

 

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

 

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

 

= (5 + 5i)/2