In Exercises 1–8, add or subtract as indicated and write the result in standard form.6 − (−5 + 4i) − (−13 − i)

Verified step by step guidance

1. Step 1: Begin by distributing the negative sign across the terms inside the parentheses: \(6 - (-5 + 4i) - (-13 - i)\).
2. Step 2: Distribute the negative sign to the first set of parentheses: \(6 + 5 - 4i\).
3. Step 3: Distribute the negative sign to the second set of parentheses: \(6 + 5 - 4i + 13 + i\).
4. Step 4: Combine the real parts: \(6 + 5 + 13\).
5. Step 5: Combine the imaginary parts: \(-4i + i\).

Key Concepts

Complex Numbers

Complex numbers are numbers that have a real part and an imaginary part, expressed in the form a + bi, where a is the real part and b is the coefficient of the imaginary unit i (where i is the square root of -1). Understanding how to manipulate complex numbers is essential for performing operations like addition and subtraction.

Addition and Subtraction of Complex Numbers

To add or subtract complex numbers, combine their real parts and their imaginary parts separately. For example, when adding (a + bi) and (c + di), the result is (a + c) + (b + d)i. This concept is crucial for simplifying expressions involving complex numbers.

Standard Form of Complex Numbers

The standard form of a complex number is a + bi, where a and b are real numbers. When performing operations on complex numbers, it is important to express the final result in this form to clearly identify the real and imaginary components, facilitating further calculations or interpretations.