![Elements Of Modern Algebra](https://www.bartleby.com/isbn_cover_images/9781285463230/9781285463230_largeCoverImage.gif)
Label each of the following statements as either true or false.
There is a one-to-one correspondence between the standard form and the trigonometric form of a
![Check Mark](/static/check-mark.png)
Whether the statement, “There is a one-to-one correspondence between the standard form and the trigonometric form of a complex number” is true or false.
Answer to Problem 1TFE
Solution:
The statement, “There is a one-to-one correspondence between the standard form and the trigonometric form of a complex number” is false.
Explanation of Solution
Consider the statement, “The standard form and the trigonometric form of a complex number show one to one correspondence”.
A complex number in standard form
Let
Therefore,
Since
Therefore,
Since more than one trigonometric form represents the same complex numbers, then there is no one-to-one correspondence between the standard form and the trigonometric form of a complex number.
Therefore, “The standard form and the trigonometric form of a complex number do not show one to one correspondence”.
Hence, the given statement is false.
Want to see more full solutions like this?
Chapter 7 Solutions
Elements Of Modern Algebra
- Elements Of Modern AlgebraAlgebraISBN:9781285463230Author:Gilbert, Linda, JimmiePublisher:Cengage Learning,Algebra for College StudentsAlgebraISBN:9781285195780Author:Jerome E. Kaufmann, Karen L. SchwittersPublisher:Cengage LearningIntermediate AlgebraAlgebraISBN:9781285195728Author:Jerome E. Kaufmann, Karen L. SchwittersPublisher:Cengage Learning
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning
![Text book image](https://www.bartleby.com/isbn_cover_images/9781285463230/9781285463230_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9781285195780/9781285195780_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9781285195728/9781285195728_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9781337278461/9781337278461_smallCoverImage.gif)