Write the complex number in standard form.
$\frac{9+\sqrt{-16}}{3}$

• A. $3+4i$
• B. $9+16i$
• C. $3+\(\frac\)43i$
• D. $\(\frac{13i}{3}\)$

Answer: (C)

Verified step by step guidance

1. Identify the given expression: \(\frac{9 + \sqrt{-16}}{3}\).
2. Recall that \(\sqrt{-16}\) can be rewritten using imaginary numbers as \(\sqrt{-16} = \sqrt{16} \times \sqrt{-1} = 4i\).
3. Substitute \(\sqrt{-16}\) with \$4i$ in the expression to get \(\frac{9 + 4i}{3}\).
4. Separate the fraction into two parts: \(\frac{9}{3} + \frac{4i}{3}\).
5. Simplify each part individually to write the complex number in standard form: \(a + bi\), where \(a = \frac{9}{3}\) and \(b = \frac{4}{3}\).