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# Complex Analysis: De Moivre's Theorem and Hyperbolic Functions

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@SprightlyVision

### What is the primary application of De Moivre's theorem in complex analysis?

• To solve quadratic equations in complex numbers
• To determine the convergence of infinite series
• To find the roots of unity
• To evaluate trigonometric functions of complex arguments (correct)
• ### What is the relationship between hyperbolic functions and trigonometric functions?

• Hyperbolic functions are unrelated to trigonometric functions
• Hyperbolic functions are a subset of trigonometric functions
• Hyperbolic functions are the inverse of trigonometric functions
• Hyperbolic functions are analogous to trigonometric functions (correct)
• ### How are the real and imaginary parts of a complex number separated?

• Using De Moivre's theorem
• Using Euler's formula
• Using the property of conjugates (correct)
• ### What is the principal value of the logarithm of a complex number?

<p>The value with the smallest argument</p> Signup and view all the answers

### What is the relationship between the logarithm of a complex number and its conjugate?

<p>They are conjugates of each other</p> Signup and view all the answers

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