Complex number need an idea to start

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SUMMARY

The discussion focuses on finding the principal value of the expression i2i. The key equation used is the principal value formula, which is Ln r + iArg(z). A crucial hint provided is that i2i can be rewritten as e2iLn(i), which simplifies the problem significantly. Understanding this transformation is essential for solving the problem accurately.

PREREQUISITES
  • Complex number theory
  • Understanding of logarithmic functions in complex analysis
  • Familiarity with Euler's formula
  • Knowledge of principal value in complex functions
NEXT STEPS
  • Study the properties of complex logarithms
  • Learn about Euler's formula and its applications
  • Explore the concept of Arg(z) in complex analysis
  • Practice solving similar problems involving complex exponentiation
USEFUL FOR

Students studying complex analysis, mathematicians interested in advanced algebra, and anyone looking to enhance their understanding of complex exponentiation and logarithms.

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Homework Statement



Find the principal value of i^2i

Homework Equations



principal value = Ln r + iArg(z)

The Attempt at a Solution


dont know how to start..
 
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Hint: [itex]i^{2i} = e^{2i\ln{i}}[/itex]
 

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