**Question 2: Complex Numbers**Given $ i^{3n+1} = -1 $, where $ i = \sqrt{-1} $, determine which of the following values of $ n $ is a solution.### Possible Answers:1. $ n = 1 $2. $ n = 2 $3. $ n = 3 $4. $ n = 4 $### Explanation:To solve this, recall the powers of $ i $:- $ i^1 = i $- $ i^2 = -1 $- $ i^3 = -i $- $ i^4 = 1 $- $ i^5 = i $ and so forth, repeating every four terms.Use this repetition to test each given $ n $ value.To confirm:1. For $ n = 1 $: $ i^{3(1)+1} = i^4 = 1 $ (which is not -1)2. For $ n = 2 $: $ i^{3(2)+1} = i^7 = i^3 = -i $ (which is not -1)3. For $ n = 3 $: $ i^{3(3)+1} = i^{10} = i^2 = -1 $, which is indeed correct.4. For $ n = 4 $: $ i^{3(4)+1} = i^{13} = i $ (which is not -1)Thus, the correct value is:\[ \boxed{n = 3} \]This exercise assesses understanding of complex number powers and cyclicity.

Given that, i3n+1=-1, where i=-1

Answered: 2. If i3n+1 = -1, where i = √√-1, then…

2. If i3n+1 = -1, where i = √√-1, then which of the following is a solution for n? (1) n = 1 (3) n = 3 (2) n = 2 (4) n = 4

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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