Question

subtract.

\\(3 + 8i) - (4 - 9i)\\

\\(3 + 8i) - (4 - 9i) = \square\\
(simplify your answer. type your answer in the form \\(a + bi\\))

Explanation:

🆕 New Concept Discovered: Operations with Complex Numbers
Combining real parts and imaginary parts separately.

Step 1: Distribute the negative sign

To subtract the second complex number, distribute the negative sign to both terms inside the parentheses:

$$ -(4 - 9i) = -4 + 9i $$

Now rewrite the entire expression without parentheses:

$$ 3 + 8i - 4 + 9i $$

Step 2: Group like terms

Group the real parts together and the imaginary parts together:

$$ (3 - 4) + (8i + 9i) $$

Step 3: Simplify

Combine the real numbers and the imaginary coefficients:

$$ 3 - 4 = -1 $$

$$ 8i + 9i = 17i $$

Combining these gives the final simplified form:

$$ -1 + 17i $$

Answer:

$$ -1 + 17i $$