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sara_87
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Homework Statement
What are the roots of
z^n = -1
Homework Equations
The Attempt at a Solution
are they
e^{\frac{2\pi k i}{n}-\frac{i \pi}{n}}
?
What Are the Roots of z^n = -1 in Complex Numbers?
- Thread starter sara_87
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SUMMARY
The roots of the equation z^n = -1 in complex numbers are given by the formula e^{\frac{2\pi k i}{n}-\frac{i \pi}{n}}. This expression is valid for all integer values of k in the range [0, n). The solution indicates that there are n distinct nth roots of -1, confirming the periodic nature of complex exponentials in the context of roots of unity.
PREREQUISITES- Complex number theory
- Understanding of Euler's formula
- Knowledge of roots of unity
- Familiarity with exponential functions in complex analysis
- Study the properties of complex exponentials
- Learn about roots of unity in detail
- Explore applications of complex numbers in engineering
- Investigate the geometric interpretation of complex roots
Mathematics students, educators, and anyone studying complex analysis or exploring the properties of complex numbers and their applications.
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