How can we simplify (2+3i)(1-i)/(3-3i)?

Given the complex
number:

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

First
we will simplify the numerator by opening the
brackets.

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

But i^2 = -1

==>
(2+3i)(1-i) = 2 +i +3 = 5+i

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

Now we will multiply numerator and denominator
by (3+3i)

==> (5+i)(3+3i)/(3-3i)(3+3i) =
(15+15i+3i+3i^2)/(9+9)

                                             =
(12+18i) / 18

                                             
= 12/18 +
i

                                               = 2/3 +
i

==> Then the value of
(2+3i)(1-i)/(3-3i) can be simplifies into the form (2/3) +
i