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This question deals with complex numbers. (a) Find the cubic roots of √5 + i√13, namely all the complex numbers z such that z³ = √5 + i√13 Express the roots in polar form. Note: You could use approximations of angles in this question. (b) Find all the exact solutions of the equation x³ - 20x² + 122x - 312 = 0, including the complex solutions. It is known that x = 12 is a solution. Express the complex solutions in Cartesian form.

This question deals with complex numbers. (a) Find the cubic roots of √5 + i√13, namely all the complex numbers z such that z³ = √5 + i√13 Express the roots in polar form. Note: You could use approximations of angles in this question. (b) Find all the exact solutions of the equation x³ - 20x² + 122x - 312 = 0, including the complex solutions. It is known that x = 12 is a solution. Express the complex solutions in Cartesian form.

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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This question deals with complex numbers. (a) Find the cubic roots of √5 + i√13, namely all the complex numbers z such that z³ = √5 + i√13 Express the roots in polar form. Note: You could use approximations of angles in this question. (b) Find all the exact solutions of the equation x³ - 20x² + 122x - 312 = 0, including the complex solutions. It is known that x = 12 is a solution. Express the complex solutions in Cartesian form.
Transcribed Image Text:This question deals with complex numbers. (a) Find the cubic roots of √5 + i√13, namely all the complex numbers z such that z³ = √5 + i√13 Express the roots in polar form. Note: You could use approximations of angles in this question. (b) Find all the exact solutions of the equation x³ - 20x² + 122x - 312 = 0, including the complex solutions. It is known that x = 12 is a solution. Express the complex solutions in Cartesian form.
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