Introduction to Complex Numbers!!...in a Calculus Course?!?
• Van Aubel's Theorem has a Beautiful a... . I love complex numbers! Complex numbers, involving the imaginary unit i (i^2=-1), are so beautiful and useful, I wanted to introduce them to students in my Calculus 2 course. A complex number takes the form a + bi, where a and b are real numbers (a, b ∈ ℝ). The real number "a" is called the real part of the complex number a + bi and the real number b is called the imaginary part of the complex number a + bi. We add and subtract complex numbers by adding and subtracting their corresponding real and imaginary parts. Geometrically, this can be interpreted using the parallelogram law for vectors. We multiply two complex numbers using FOIL and the fact that i^2=-1. And we divide two complex numbers by multiplying the numerator and the denominator of the resulting complex number fraction by the complex conjugate of the denominator.
Calculus 2, Lecture 28E
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