Question

find the sum of \\(-4 + i\\) and \\(10 - 5i\\).

• \\(-3 + 5i\\)
• \\(-3 - 5i\\)
• \\(6 - 4i\\)
• \\(6 - 6i\\)

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 addition

To find the sum, we write the two complex numbers together in an addition expression:

$$ (-4 + i) + (10 - 5i) $$

Step 2: Group like terms

Complex numbers have two parts: a real part (the regular numbers) and an imaginary part (the terms with \(i\)). We group the real parts together and the imaginary parts together:

$$ (-4 + 10) + (1i - 5i) $$

Step 3: Simplify each group

Now, we calculate the sum for each part:

• Real parts: \(-4 + 10 = 6\)
• Imaginary parts: \(1i - 5i = -4i\)

Combining these gives:

$$ 6 - 4i $$

Answer:

\(6 - 4i\) (the third option)