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: \(8i + 9i\) and \(-14\).
4. Add the imaginary parts: \(8i + 9i = 17i\).
5. Write the expression in standard form: \(-14 + 17i\).

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, which is defined as the square root of -1. Understanding complex numbers is essential for performing operations such as addition and subtraction.

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, the goal is to express the result in this standard form, which makes it easier to interpret and use in further calculations.

Distributive Property

The distributive property states that a(b + c) = ab + ac, allowing us to multiply a single term by each term within parentheses. This property is crucial when simplifying expressions involving complex numbers, as it helps in correctly distributing negative signs and combining like terms.