To solve this, let’s express the given complex number $-2 + \sqrt{-18}$ in standard form.

Step-by-step Solution:

1. Simplify the square root: $\sqrt{-18} = \sqrt{18} \cdot i$ where $i = \sqrt{-1}$.

2. Break down $\sqrt{18}$: $\sqrt{18} = \sqrt{9 \cdot 2} = \sqrt{9} \cdot \sqrt{2} = 3\sqrt{2}.$

   Substituting back: $\sqrt{-18} = 3\sqrt{2}i.$

3. Write in standard form: The given number becomes: $-2 + 3\sqrt{2}i.$

Answer:

The correct option is d: $-2 + 3\sqrt{2}i$.

Would you like a detailed explanation of this process or help with related topics?

Related Questions:

1. How can you simplify the square root of a negative number systematically?
2. What is the general process for converting a number with imaginary parts into standard form?
3. Why does $i^2 = -1$, and how is it used in simplifying roots?
4. How do we split radicals like $\sqrt{18}$ into simpler components?
5. What is the significance of standard form in complex numbers?

Tip:

Always simplify the square root of a negative number using $i$ before combining it with other terms to ensure correct results.