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.