1. Let a, b, c E R, and w' = 1, with w # 1 has strictly positive imaginary part. If a, b, c are not all different then prove that (a + bw + cw²)³ is real Hint: preliminary working is covered in the workshop tasks!

1. Let a, b, c E R, and w' = 1, with w # 1 has strictly positive imaginary part. If a, b, c are not all different then prove that (a + bw + cw²)³ is real Hint: preliminary working is covered in the workshop tasks!

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.3: Eigenvalues And Eigenvectors Of N X N Matrices

Problem 14EQ

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Let a,b,c∈R, and w^3=1, with w /= 1 has strictly positive imaginary part. If a,b,c are not all different then prove that (a+bw+cw^2)^3 is real.

1. Let a, b, c E R, and w
1, with w + 1 has strictly positive imaginary part. If a, b, c are not all different then prove that (a + b@ + co²)³ is real.
Hint: preliminary working is covered in the workshop tasks!

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