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

• A. $3+4i$
• B. $9+16i$
• C. $3+\frac43i$
• D. $\frac{13i}{3}$

Answer: (C)

Verified step by step guidance

1. Identify the expression given: \(\frac{9 + \sqrt{-16}}{3}\). Notice that the square root of a negative number involves imaginary numbers.
2. Rewrite the square root of the negative number using the imaginary unit \(i\), where \(i = \sqrt{-1}\). So, \(\sqrt{-16} = \sqrt{16} \times \sqrt{-1} = 4i\).
3. Substitute \(\sqrt{-16}\) with \$4i\( in the original expression to get \)\frac{9 + 4i}{3}$.
4. Separate the fraction into two parts: \(\frac{9}{3} + \frac{4i}{3}\).
5. Simplify each fraction individually to write the complex number in standard form: \(a + bi\), where \(a\) and \(b\) are real numbers.