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Solve and check each linear equation. 3(x - 1) = 21
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Ch. 1 - Equations and Inequalities
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Capitolo 2, Problema 5
In Exercises 1–8, add or subtract as indicated and write the result in standard form. 6 - (- 5 + 4i) - (- 13 - i)
Guida verificata passo dopo passo1
Identify the expression to simplify: \(6 - (-5 + 4i) - (-13 - i)\).
Apply the distributive property to remove the parentheses by changing the signs inside each set of parentheses preceded by a minus sign: \(6 + 5 - 4i + 13 + i\).
Group the real parts together and the imaginary parts together: \((6 + 5 + 13) + (-4i + i)\).
Add the real numbers: \(6 + 5 + 13\), and add the imaginary coefficients: \(-4 + 1\).
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.
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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.
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05:02
Multiplying Complex Numbers
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.
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03:18Adding and Subtracting Complex Numbers
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.
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04:15Multiply Polynomials Using the Distributive Property
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