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Prove that (1+i)" + 1(1- i)" = 2m/2*1 nt cos 4

Prove that (1+i)" + 1(1- i)" = 2m/2*1 nt cos 4

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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**Prove that:** \[ (1+i)^n + (1-i)^n = 2^{(\pi / 2) + 1} \cos\left( \frac{n\pi}{4} \right) \] **Explanation:** The formula presents a mathematical expression involving complex numbers, exponents, and trigonometric functions. The expression on the left involves the sum of complex numbers raised to an integer power \( n \). The expression on the right is formatted as a power of 2 multiplied by a cosine function, which also incorporates the variable \( n \), a constant \(\pi\), and a trigonometric angle divided by 4. The equation is set up to explore the relationship between these complex numbers and trigonometric identities. To prove this equation, one may need to use properties of complex numbers, De Moivre's Theorem, and trigonometric identities.
Transcribed Image Text:**Prove that:** \[ (1+i)^n + (1-i)^n = 2^{(\pi / 2) + 1} \cos\left( \frac{n\pi}{4} \right) \] **Explanation:** The formula presents a mathematical expression involving complex numbers, exponents, and trigonometric functions. The expression on the left involves the sum of complex numbers raised to an integer power \( n \). The expression on the right is formatted as a power of 2 multiplied by a cosine function, which also incorporates the variable \( n \), a constant \(\pi\), and a trigonometric angle divided by 4. The equation is set up to explore the relationship between these complex numbers and trigonometric identities. To prove this equation, one may need to use properties of complex numbers, De Moivre's Theorem, and trigonometric identities.
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