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. Group the real parts and the imaginary parts separately: \((-14) + (8i + 9i)\).
4. Combine like terms: the real part remains \(-14\), and the imaginary parts add up to \$17i$.
5. Write the final expression in standard form \(a + bi\): \(-14 + 17i\).

Key Concepts

Complex Numbers and Standard Form

Complex numbers are expressed in the form a + bi, where a is the real part and b is the imaginary part. Writing the result in standard form means combining like terms so the expression is clearly separated into real and imaginary components.

Distributive Property

The distributive property allows you to remove parentheses by multiplying a term outside the parentheses by each term inside. For example, subtracting (14 - 9i) means distributing the negative sign to both 14 and -9i.

Combining Like Terms

After distributing, combine the real parts together and the imaginary parts together. This simplifies the expression into a single complex number in standard form, making it easier to interpret and use.