In Exercises 1–8, add or subtract as indicated and write the result in standard form.8i − (14 − 9i)

Verified step by step guidance

1. Identify the expression to simplify: \(8i - (14 - 9i)\).
2. Distribute the negative sign across the terms inside the parentheses: \(8i - 14 + 9i\).
3. Combine like terms by adding the imaginary parts: \(8i + 9i\).
4. Combine the real parts: \(-14\).
5. Write the result in standard form \(a + bi\), where \(a\) is the real part and \(b\) is the imaginary part.

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, b is the imaginary part, and i is the imaginary unit defined as the square root of -1. Understanding complex numbers is essential for performing operations such as addition and subtraction.

Addition and Subtraction of Complex Numbers

To add or subtract complex numbers, you 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. Writing complex numbers in this form helps in clearly identifying the real and imaginary components, which is important for further mathematical operations and interpretations.