Practice Exercises - | 5. Complex Exponential Function | Mathematics (Civil Engineering -1)
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- Exercises

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

Show that eiπ + 1 = 0 using Euler’s formula.

💡 Hint: Remember what Euler's formula states!

Question 2

Easy

Express cos(3x) in terms of exponential functions.

💡 Hint: Recall the definition of cosine in exponential form.

Practice 4 more questions and get performance evaluation

Interactive Quizzes

Engage in quick quizzes to reinforce what you've learned and check your comprehension.

Question 1

What does Euler's formula state?

  • e^(ix) = cos(x) + i*sin(x)
  • e^(ix) = cos(x) - i*sin(x)
  • e^(ix) = i*cos(x) + sin(x)

💡 Hint: Focus on the relationship between complex numbers and trigonometric functions.

Question 2

True or False: The roots of a complex number can be evenly spaced on a circle.

  • True
  • False

💡 Hint: Think about how roots are derived and their geometric representation.

Solve 1 more question and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

A high-rise building vibrates due to wind forces modeled by the differential equation d²y/dx² + λy = 0. Determine the form of the solution if λ = 16, and explain the physical meaning of the terms.

💡 Hint: Identify how roots relate to the oscillation frequency.

Question 2

Transform the following expression into exponential form: sin(2x) + cos(2x). What's the geometric interpretation of this expression on the complex plane?

💡 Hint: Consider how both sine and cosine contribute to a single complex circle.

Challenge and get performance evaluation