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Chapter 8: Problem 105

Describe how to multiply conjugates.

Short Answer

Expert verified
Multiplication of the conjugates \(a + b\) and \(a - b\) results in the difference of squares, which is \(a^2 - b^2\).

Step by step solution

01

Identify the conjugate pair

To multiply conjugates, first identify the two expressions that make up the conjugate pair. They should have the same terms, but opposite signs. In other words, if the first expression is \(a + b\), then its conjugate would be \(a - b\), and vice versa.
02

Apply the rule of multiplying conjugates

The rule when multiplying conjugates is that it results in the difference of squares. Apply this rule to the pair of conjugates. Let's assume \(a + b\) and \(a - b\) are our pair of conjugates, hence their multiplication results in \(a^2 - b^2\). This is because when you multiply \(a + b\) and \(a - b\), the middle terms cancel out and leave only \(a^2 - b^2\).
03

Solve

Resolve \(a^2 - b^2\), where \(a\) and \(b\) are the terms from the original expressions. If \(a\) and \(b\) are real numbers or have definite values, calculate the values of \(a^2\) and \(b^2\) and subtract the latter from the former to get the result.

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