Identify the real and imaginary parts of each complex number.
$3+2i\sqrt{3}$

• A. $a=3,b=2\sqrt3$
• B. $a = 3, b = 2$
• C. $a=2\sqrt3,b=3$
• D. $a=3,b=\sqrt3$

Answer: (A)

Verified step by step guidance

1. Recall that a complex number is generally written in the form \(a + bi\), where \(a\) is the real part and \(b\) is the coefficient of the imaginary part.
2. Identify the real part \(a\) by looking at the term without the imaginary unit \(i\). In the expression \$3 + 2i\sqrt{3}\(, the real part is the constant term \)3$.
3. Identify the imaginary part \(b\) by looking at the coefficient multiplying \(i\). Here, the imaginary part coefficient is \$2\sqrt{3}\( because it multiplies \)i$.
4. Write down the real part and imaginary part separately: \(a = 3\) and \(b = 2\sqrt{3}\).
5. Thus, the complex number \$3 + 2i\sqrt{3}\( has a real part of \)3\( and an imaginary part of \)2\sqrt{3}$.