How Do You Simplify the Square of Complex Conjugates?

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SUMMARY

The discussion focuses on simplifying the expression (\sqrt{3+4i}+\sqrt{3-4i})^{2}. The key steps involve recognizing that (\sqrt{3+4i})(\sqrt{3-4i}) simplifies to \sqrt{(3+4i)(3-4i)}, which is the product of a complex number and its conjugate. This leads to the simplification of the square root term, ultimately resulting in a clearer path to the final answer.

PREREQUISITES
  • Understanding of complex numbers and their conjugates
  • Familiarity with the properties of square roots
  • Basic algebraic expansion techniques
  • Knowledge of simplifying expressions involving complex numbers
NEXT STEPS
  • Learn about the properties of complex conjugates in detail
  • Study the process of simplifying square roots of complex numbers
  • Explore algebraic identities related to complex numbers
  • Practice problems involving the expansion of binomials with complex numbers
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Students studying complex numbers, mathematics enthusiasts, and anyone looking to improve their skills in simplifying expressions involving complex conjugates.

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Homework Statement



Simplify ([itex]\sqrt{3+4i}[/itex]+[itex]\sqrt{3-4i}[/itex])[itex]^{2}[/itex]



Homework Equations





The Attempt at a Solution



well I tried expanding it out but I don't think that is the right approach but I have no other idea to tackle the problem?

so by expanding I had 6+2([itex]\sqrt{3+4i}[/itex])([itex]\sqrt{3-4i}[/itex])

But then I didnt know where to go

please help!
 
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[tex](\sqrt{3+4i})(\sqrt{3-4i})=\sqrt{(3+4i)(3-4i)}[/tex]

Now how can you simplify the term in the sqrt? Notice we have a complex number multiplied by it's complex conjugate
 

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