Substituting an Imaginary Number in a Rational Function

Let $f (x) = \frac{2 + x}{x + 3} .$ Evaluate $f (10 i) .$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
Substitute $x = 10 i$ and simplify.

$\begin{array}{l} \frac{2 + 10 i}{10 i + 3} & Substitute 10 i for x . \\ \frac{2 + 10 i}{3 + 10 i} & Rewrite the denominator in standard form . \\ \frac{2 + 10 i}{3 + 10 i} \cdot \frac{3 - 10 i}{3 - 10 i} & Prepare to multiply the numerator and \\ denominator by the complex conjugate \\ of the denominator . \\ \frac{6 - 20 i + 30 i - 100 i^{2}}{9 - 30 i + 30 i - 100 i^{2}} & Multiply using the distributive property or the FOIL method . \\ \frac{6 - 20 i + 30 i - 100 (- 1)}{9 - 30 i + 30 i - 100 (- 1)} & Substitute –1 for i^{2} . \\ \frac{106 + 10 i}{109} & Simplify . \\ \frac{106}{109} + \frac{10}{109} i & Separate the real and imaginary parts . \end{array}$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Let $f (x) = \frac{x + 1}{x - 4} .$ Evaluate $f (- i) .$

How did it go?