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. Identify the expression to simplify: \$6 - (-5 + 4i) - (-13 - i)$.
2. Apply the distributive property to remove the parentheses by changing the signs inside each set of parentheses preceded by a minus sign: \$6 + 5 - 4i + 13 + i$.
3. Group the real parts together and the imaginary parts together: \((6 + 5 + 13) + (-4i + i)\).
4. Add the real numbers: \$6 + 5 + 13\(, and add the imaginary coefficients: \)-4 + 1$.
5. Write the final expression in standard form \(a + bi\), where \(a\) is the sum of the real parts and \(b\) is the sum of the imaginary coefficients.

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 a complex number in standard form means arranging it as a + bi, which helps in clearly identifying and combining like terms.

Addition and Subtraction of Complex Numbers

To add or subtract complex numbers, combine their real parts separately and their imaginary parts separately. This process is similar to combining like terms in algebra, ensuring the result remains in standard form.

Distributive Property and Handling Negative Signs

When subtracting complex numbers, apply the distributive property to remove parentheses, especially when a negative sign precedes a parenthesis. Correctly handling negative signs is crucial to avoid errors in combining terms.