Ch. 1 - Equations and Inequalities

Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook

Lial 13th Edition

Ch. 1 - Equations and Inequalities

Problem 21

Chapter 2, Problem 21

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

Verified step by step guidance

Identify the expression to simplify: $15i - (3 + 2i) - 11$.

Distribute the negative sign across the parentheses: $15i - 3 - 2i - 11$.

Group the real parts together and the imaginary parts together: $(-3 - 11) + (15i - 2i)$.

Combine the like terms: $-14 + 13i$.

Write the final answer in standard form: $a + bi$, where $a = -14$ and $b = 13$.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.

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