# Mathematical and Computational Methods in Physics and Engineering (fall 2016)

## Daily outline for Wed, Sep 14, 2016 9:10 AM (1 year ago)

### Complex numbers 1

assigned today:

Due today:

First we talked about how humanity has invented numbers. The two common guesses at the order were:

1. positive integers
2. negative integers
3. rationals
4. irrationals
5. complex numbers

and

1. positive integers
2. rationals
3. negative integers
4. irrationals
5. complex numbers

with unanimous consensus on the first and last ones. I asked if they could imagine pi rocks or 3+7i rocks, noting that we don't really use complex numbers for counting.

During the quiz (curve fitting again) I jotted down the things I thought we should hit today:

• complex operations (+, -, etc)
• new operations (complex conjugate, absolute value, etc)
• Plotting (Argand diagrams)
• Euler
• powers
• roots
• rotation

I asked them to write the two that they were least confident about. Euler got a lot of votes until I reminded/told them that $$e^{i\theta}=\cos\theta+i\sin\theta$$. Mostly it was about roots and rotations.

I asked them to draw a random z on an Argand diagram and then to draw where i times z would be. We then talked about why multiplying by i is the same as a positive 90 degree rotation. I asked what multiplying by a random z would do and we talked about rotation, stretch, and translation (noting that you don't really need the translation part).

We were running out of time so we quickly hit powers ($$z^n=r^n(\cos n\theta+\sin n\theta)$$) and roots. They asked for a resource on roots.

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