If

\[ \frac{(8  i)}{(3  2i)}\]

can be written in the form a + bi, where a and b are real numbers, what is the value of a?
A) 2 B) 8/3 C) 3 D) 11/3 
Answer:
Multiply the numerator and denominator of the expression
by the conjugate (3  2i), which is (3 + 2i).

\[ \frac{(8  i)}{(3  2i)}\]

This results in the following.
\[ \frac{(8  i) * ( 3 + 2i)}{(3  2i) * ( 3 + 2i)} = \frac{24 + 16i  3i + (i)(2i)}{(3^2)  (2i ^2)}\]
The above expression can be reduced to

\[ \frac{24 + 16i  3i + (i)(2i)}{(9)  (4)} = \frac{26 + 13i}{13} \]

which further simplifies to 2 + i, and when written in the form a + bi means that a = 2, and the answer is A).