Question

subtract \\((3 + 2i)\\) from \\((-9 - 8i)\\).

\\(\bigcirc\\) \\(-27 - 5i\\)
\\(\bigcirc\\) \\(-6 - 6i\\)
\\(\bigcirc\\) \\(-12 - 10i\\)
\\(\bigcirc\\) \\(12 + 10i\\)

Explanation:

🆕 New Concept Discovered: Operations with Complex Numbers
Combine real parts with real parts, and imaginary parts with imaginary parts.

Step 1: Set up the subtraction expression

To subtract \( (3 + 2i) \) from \( (-9 - 8i) \), we write the expression as:

$$ (-9 - 8i) - (3 + 2i) $$

Step 2: Distribute the negative sign

Distribute the negative sign to both terms inside the second set of parentheses:

$$ -9 - 8i - 3 - 2i $$

Step 3: Group and combine like terms

Group the real parts together and the imaginary parts together:

$$ (-9 - 3) + (-8i - 2i) $$

Combine the real numbers:

$$ -9 - 3 = -12 $$

Combine the imaginary numbers:

$$ -8i - 2i = -10i $$

Combining these results gives:

$$ -12 - 10i $$

Answer:

\( -12 - 10i \) (the third option)