Practice - Complex Exponential Function - 5
Enroll to start learning
You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.
Practice Questions
Test your understanding with targeted questions
Show that e^(iπ) + 1 = 0 using Euler’s formula.
💡 Hint: Think about the values of cosine and sine at π.
Express cos(3x) using exponential functions.
💡 Hint: Use Euler's formula.
3 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What does Euler's formula state?
💡 Hint: Remember, it connects e^(ix) with both cosine and sine.
True or False: The modulus of e^(x + iy) is |e^x|.
💡 Hint: Consider the definition of modulus for complex numbers.
Get performance evaluation
Challenge Problems
Push your limits with advanced challenges
Prove that e^(iθ) has a modulus of 1 for any real θ. What does this imply about its representation on the complex plane?
💡 Hint: Check the properties of sine and cosine for their squared sums.
Use the properties of complex exponentials to solve for solutions to the equation d²y/dt² + 16y = 0, discussing its relationship to oscillatory motion.
💡 Hint: Think about the connections between roots and oscillation frequency.
Get performance evaluation
Reference links
Supplementary resources to enhance your learning experience.