If $a = 2 + 3i$ and $b = 1 − i$, compute each of the following operations:

1. $a + b$

   Hint (a):

   $\left(2 + 3i\right) + \left(1 − i\right)$

   Answer (a):

   $3 + 2i$

2. $a − b$

   Hint (b):

   $\left(2 + 3i\right) − \left(1 − i\right)$
   Use a generic rectangle.

3. $ab$

   Hint (c):

   $\left(2 + 3i\right)\left(1 − i\right)$

4. $\frac{a}{b}$

   Hint (d):

   $\frac{(2+3i)}{(1-i)}\ \ \ \ \ \ \ \ \ \ \ =\frac{(2+3i)}{(1-i)}\cdot\frac{(1+i)}{(1+i)}$

   Answer (d):

   $-\frac{1}{2}+\frac{5}{2}i$