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Determine whether the statement is true or false.
The product of a
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Whether the statement “The product of a complex number and its conjugate is a real number” is true or false.
Answer to Problem 1MC
The given statement is true.
Explanation of Solution
Definitions used:
The number i:
The number i is defined such that
To express roots of negative numbers in terms of i, we can use the fact that
Conjugate of a complex number:
The conjugate of a complex number
Calculation:
Consider the complex number
The conjugate of
Evaluate the product as follows.
Here,
Thus, the product of a complex number and its conjugate is a real number.
Therefore, the given statement is true.
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Chapter 3 Solutions
College Algebra: Graphs and Models, Books a la Carte Edition plus MyLab Math with Pearson eText -- Access Card Package (6th Edition)
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage