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4-2) Given that z = 2 (cos(+j sin ()) satisfies the equation z* = c(1 + j√3), where c is re a. Find the value of c. b. Find the other three roots of this equation. c. Express the roots in exponential and polar forms. Hint: Use de Moivre's Theorem to find the value of z4 then equate the two equations.

4-2) Given that z = 2 (cos(+j sin ()) satisfies the equation z* = c(1 + j√3), where c is re a. Find the value of c. b. Find the other three roots of this equation. c. Express the roots in exponential and polar forms. Hint: Use de Moivre's Theorem to find the value of z4 then equate the two equations.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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4-2) Given that z = 2(cos () + j sin () satisfies the equation z* = c(1+jv3), where c is real a. Find the value of c. b. Find the other three roots of this equation. c. Express the roots in exponential and polar forms. Hint: Use de Moivre's Theorem to find the value of z* then equate the two equations. 4-3) Use de Moivre's theorem to test the correctness of the following trigonometric identity: sin?(50) csc(50) 5 tan(0) – 10 tan³ (0) + tan (0) cos (50) 1– 10 tan? (0) + 5 tanª(0)
Transcribed Image Text:4-2) Given that z = 2(cos () + j sin () satisfies the equation z* = c(1+jv3), where c is real a. Find the value of c. b. Find the other three roots of this equation. c. Express the roots in exponential and polar forms. Hint: Use de Moivre's Theorem to find the value of z* then equate the two equations. 4-3) Use de Moivre's theorem to test the correctness of the following trigonometric identity: sin?(50) csc(50) 5 tan(0) – 10 tan³ (0) + tan (0) cos (50) 1– 10 tan? (0) + 5 tanª(0)
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