Checkpoint: Identities with Complex Numbers Solution

Find the value of Q that makes the proportion equal.

$\frac{Q}{3 + i} = \frac{33 - 11 i}{10}$

$\begin{array}{rcl} 10 Q & = & (3 + i) (33 - 11 i) \\ 10 Q & = & 99 - 33 i + 33 i - 11 i^{2} \\ 10 Q & = & 99 - 11 (- 1) \\ 10 Q & = & 110 \\ Q & = & 11 \end{array}$

Note

Cross-product
Simplify expression on right side
Solve for Q

Note

Q: Why is this not a polynomial?

A: Polynomials cannot have denominators that are not rationalized.