Day 98

Spent a good amount of time trying to figure out complex number multiplication..

For example : (a + b i ) * (a2 + b2 i ), can be expressed in terms of the angles being added and the magnitudes being multiplied right.

You could also think of the final vector as

the real part – (a*a2) – (b*b2) and

the imaginary part – (a*b2 i ) + (b i * a2)

Or you could also think of them like vectors being stretched and added

So the original imaginary number (a + b i ) |

is being scaled by a real number: a2 and

an imaginary number : b2 i (Which rotates the vector by 90 degrees)

and then added together.

I honestly don’t know what I was trying to figure out but I worked for almost 2 hours trying to figure out why Sin and Cos show up in this relationship… I’m pretty weak at trigonometry so I see this as a kind of way to develop intuition for what’s happening. Hope it wasn’t all a big waste of time haha.