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 complex number given in the problem: \( \frac{9 + \sqrt{-16}}{3} \).
2. Recognize that \( \sqrt{-16} \) can be expressed using the imaginary unit \( i \), where \( \sqrt{-16} = 4i \).
3. Substitute \( \sqrt{-16} \) with \( 4i \) in the expression: \( \frac{9 + 4i}{3} \).
4. Separate the real and imaginary parts of the complex number: \( \frac{9}{3} + \frac{4i}{3} \).
5. Simplify each part to write the complex number in standard form: \( 3 + \frac{4}{3}i \).