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Let a, 6 be positive real numbers with a E Z. The set of values represented by i+0 lie on a ray whose argument is 5 None of the given options is correct a circle a ray whose argument is a ray whose argument is

Let a, 6 be positive real numbers with a E Z. The set of values represented by i+0 lie on a ray whose argument is 5 None of the given options is correct a circle a ray whose argument is a ray whose argument is

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Transcription for Educational Website:** --- **Mathematical Problem:** Let \( a, b \) be positive real numbers with \( a \in \mathbb{Z} \). The set of values represented by \( i^{a-ib} \) lies on: 1. \( \bigcirc \) a ray whose argument is \( \frac{\pi}{2} \) 2. \( \bigcirc \) None of the given options is correct 3. \( \bigcirc \) a circle 4. \( \bigcirc \) a ray whose argument is \( \frac{\pi a}{2} \) 5. \( \bigcirc \) a ray whose argument is \( \frac{\pi b}{2} \) --- In this problem, we are given two positive real numbers \( a \) and \( b \), with \( a \) specified as an integer (\( a \in \mathbb{Z} \)). We need to determine the nature of the set of values represented by the expression \( i^{a-ib} \). **Options Analysis:** - The first option suggests that the values lie on a ray whose argument is \( \frac{\pi}{2} \). - The second option states that none of the given options is correct. - The third option indicates that the values lie on a circle. - The fourth option mentions a ray whose argument is \( \frac{\pi a}{2} \). - The fifth option implies a ray whose argument is \( \frac{\pi b}{2} \). To determine the correct option, one must analyze the mathematical implications of the expression \( i^{a-ib} \). **Graphical and Diagram Explanation:** There are no graphs or diagrams included in this problem statement. The given options are purely textual. --- **Note for Students:** Review the principles of complex numbers and their representation to correctly analyze each provided option and determine where the set of values represented by \( i^{a-ib} \) lies.
Transcribed Image Text:**Transcription for Educational Website:** --- **Mathematical Problem:** Let \( a, b \) be positive real numbers with \( a \in \mathbb{Z} \). The set of values represented by \( i^{a-ib} \) lies on: 1. \( \bigcirc \) a ray whose argument is \( \frac{\pi}{2} \) 2. \( \bigcirc \) None of the given options is correct 3. \( \bigcirc \) a circle 4. \( \bigcirc \) a ray whose argument is \( \frac{\pi a}{2} \) 5. \( \bigcirc \) a ray whose argument is \( \frac{\pi b}{2} \) --- In this problem, we are given two positive real numbers \( a \) and \( b \), with \( a \) specified as an integer (\( a \in \mathbb{Z} \)). We need to determine the nature of the set of values represented by the expression \( i^{a-ib} \). **Options Analysis:** - The first option suggests that the values lie on a ray whose argument is \( \frac{\pi}{2} \). - The second option states that none of the given options is correct. - The third option indicates that the values lie on a circle. - The fourth option mentions a ray whose argument is \( \frac{\pi a}{2} \). - The fifth option implies a ray whose argument is \( \frac{\pi b}{2} \). To determine the correct option, one must analyze the mathematical implications of the expression \( i^{a-ib} \). **Graphical and Diagram Explanation:** There are no graphs or diagrams included in this problem statement. The given options are purely textual. --- **Note for Students:** Review the principles of complex numbers and their representation to correctly analyze each provided option and determine where the set of values represented by \( i^{a-ib} \) lies.
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