Identify the real and imaginary parts of each complex number.
$-4-9i$

• A. $a = -9, b = -4$
• B. $a = -4, b = -9$
• C. $a = 4, b = 9$
• D. $a = -4, b = 9$

Answer: (B)

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 \(i\).
2. Identify the real part \(a\) by looking at the constant term without the imaginary unit \(i\). In the complex number \(-4 - 9i\), the real part is the number without \(i\), which is \(-4\).
3. Identify the imaginary part \(b\) by looking at the coefficient of \(i\). In \(-4 - 9i\), the coefficient of \(i\) is \(-9\), so the imaginary part is \(-9\).
4. Write down the real and imaginary parts explicitly as \(a = -4\) and \(b = -9\).
5. Verify that the complex number matches the form \(a + bi\) with your identified parts: \(-4 - 9i\) corresponds to \(a = -4\) and \(b = -9\).