Linear Dependence: Complex Equations & Conjugates

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SUMMARY

The discussion centers on the linear dependence of complex equations and their conjugates, specifically addressing the equation φ*(M² - φ²) + m²φ = 0, where m and M are real numbers. Participants explore whether the complex conjugate of this equation is a multiple of the original equation, raising questions about the definition of linear independence in this context. The conversation highlights the importance of understanding the relationship between complex numbers and their conjugates in linear algebra.

PREREQUISITES
  • Understanding of complex numbers and their properties
  • Familiarity with linear algebra concepts, specifically linear dependence and independence
  • Knowledge of complex conjugates and their mathematical significance
  • Basic grasp of algebraic equations and manipulation
NEXT STEPS
  • Study the properties of complex conjugates in linear algebra
  • Learn about linear dependence and independence in vector spaces
  • Explore the implications of complex equations in real number contexts
  • Investigate the application of complex numbers in solving polynomial equations
USEFUL FOR

Students and professionals in mathematics, particularly those studying linear algebra, complex analysis, or anyone interested in the properties of complex equations and their applications.

emanaly
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Hi All
A complex equation and its complex conjugate are linearly dependent or independent
thanks
eman
 
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Is the complex conjugate a multiple of the original number?
 
slider142 said:
Is the complex conjugate a multiple of the original number?

The equation is
\phi\ast(M^{2}-\phi^{2})+m^{2}\phi=0 where m and M are real
 
Okay, so what is its "complex conjugate"? And what does it mean to say that two equations are linearly independent?
 

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