Perform each operation. Write answers in standard form. 15i- (3+2i) -11

Verified step by step guidance

1. Identify the expression to simplify: \$15i - (3 + 2i) - 11$.
2. Distribute the negative sign across the parentheses: \$15i - 3 - 2i - 11$.
3. Group the real parts together and the imaginary parts together: \((-3 - 11) + (15i - 2i)\).
4. Combine the like terms: \(-14 + 13i\).
5. Write the final answer in standard form: \(a + bi\), where \(a = -14\) and \(b = 13\).

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 answers in standard form means presenting the result explicitly as a sum of a real number and an imaginary number.

Addition and Subtraction of Complex Numbers

To add or subtract complex numbers, combine their real parts and their imaginary parts separately. For example, (a + bi) - (c + di) = (a - c) + (b - d)i.

Distributive Property and Simplification

When subtracting expressions like 15i - (3 + 2i), apply the distributive property to remove parentheses by changing signs accordingly. Then, combine like terms to simplify the expression.