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i82

i82

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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Question
The image displays the mathematical expression \( i^{82} \). ### Explanation: The symbol \( i \) represents the imaginary unit, with the property that \( i^2 = -1 \). Any power of \( i \) repeats in a cycle of four: - \( i^1 = i \) - \( i^2 = -1 \) - \( i^3 = -i \) - \( i^4 = 1 \) To find \( i^{82} \), you determine the remainder of 82 divided by 4, as powers of \( i \) repeat every four terms. - Divide 82 by 4, which gives a remainder of 2. Thus, \( i^{82} = i^2 = -1 \).
Transcribed Image Text:The image displays the mathematical expression \( i^{82} \). ### Explanation: The symbol \( i \) represents the imaginary unit, with the property that \( i^2 = -1 \). Any power of \( i \) repeats in a cycle of four: - \( i^1 = i \) - \( i^2 = -1 \) - \( i^3 = -i \) - \( i^4 = 1 \) To find \( i^{82} \), you determine the remainder of 82 divided by 4, as powers of \( i \) repeat every four terms. - Divide 82 by 4, which gives a remainder of 2. Thus, \( i^{82} = i^2 = -1 \).
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