[ Solutions to problems 1 2 3 4 5 6 7 8 9 10 | Lecture 1 | Home | Instructor ]

# Lecture 1: Exercises

• Complex arithmetic: Lyons (chap. 4), Arfken (chap. 6.1)
• Infinite series: Arfken (chap. 5.1)

### Questions for Review

• Do all quadratic equations have a real solution? Give examples!
• What is the imaginary unit?
• What is a complex number?
• How can complex numbers be represented graphically?
• How does one calculate the absolute value and the argument of a complex number?
• How does one add complex numbers? How can this addition be represented graphically?
• What is the triangle inequality?
• How does one multiply complex numbers? What are the absolute value and the argument of a product of complex numbers?
• What is the inverse of a complex number? What are its absolute value and its argument?
• How is the complex conjugate of a complex number defined? What does this correspond to graphically?
• What is the complex conjugate of a sum/product of complex numbers?
• What is an infinite sequence? How can an infinite sequence be represented?
• What does it mean to say that an infinite sequence converges?
• What is a monotonic sequence? Under which conditions does it converge?
• What is an infinite series? Give examples!
• What does it mean to say that an infinite series converges?
• What is the geometric series? Does it converge? Why?
• What is the harmonic series? Does it converge? Why?