In a sense, you need complex numbers to live. This is because complex numbers are intimately connected to periodic phenomena such as beating hearts and planetary motion. More widely, complex numbers are used in physics, chemistry, biology, economics, electrical engineering, statistics, and many different areas of mathematics. One beautiful example comes from fractals. Check out this movie of the Mandelbrot set.
By the end of this lesson, you should be able to:
- Define complex numbers.
- Perform algebraic operations on complex numbers.
- Interpret complex numbers and complex arithmetic geometrically.
- Apply Euler's formula.
- Convert between cartesian and polar representations of complex numbers.
- Use Euler's formula to derive trigonometric identities.
- Read excerpt from O'Neil.
- Watch pencasts (the links above are identical, and all point to one combined file).
- Check yourself before you wreck yourself.
After class, please:
- Do these problems.