Checkpoint: Rationalizing Denominators with Complex Numbers Solution

Simplify.

$\frac{6 i}{2 + 7 i}$

$\begin{array}{rcl} \frac{6 i}{2 + 7 i} (\frac{2 - 7 i}{2 - 7 i}) & = & \frac{12 i - 42 i^{2}}{4 - 49 i^{2}} \\ \frac{12 i - 42 (- 1)}{4 - 49 (- 1)} & = & \frac{42 + 12 i}{53} \end{array}$

Note

Q: How do you rationalize the denominator for this problem?

A: Multiply the entire fraction by the complex conjugate.