is anybeing here capable of telling me what the hell is going on with DeMoivre's Theorem. Or the trigonomic forms of complex numbers in general. The fuck
Like. Ok. You have z = numberx +/- numbery i
So u put that with x and y under a radical while squaring both. You get r, which u use later
then for whatever reason you use tangent (angle sign) equaling to y / x. Find answer. Sure. Then,, then???
for whatever reason you use that answer to get whatever y/x corresponds with on the unit circle. I can't see a purpose for this
then you end up with the angle equaling some other bullshit from the unit circle(?). I cant tell where this comes from
then you put it into the final equation, as
z = r (cos (angle) + sin (angle))
except when there's only one number in the original prompt. Then you don't...?? And you substitute the non-i number with zero in the finding-r-equation. Again, i don't know how the hell to find what the angle equals. The second step from before is simply labeled "unhelpful" (presumably because of the zero in the denominator) but no further explanation is given.
doing it the opposite way you just distribute the r into the rest of the equation. Simple enough, probably
something called "trig form", left unexplained... i kinda get it though?
i kiiin of get demoivres theorem. You just multiply the angles of cos and sin by the power, rather than using it as a power, and instead only use it as a power on r. Then you convert the angles to..... the corresponding x or y on the unit circle for that angle?? Is that it?? Then distribute the new r, leaving it as the original x +/- y i from above. Interesting
Except when you don't do that, cuz its in radian form, so you convert it..... into...??? Decimals???? How?? Just in the calculator maybe?
i can't reliably grasp well enough to talk through what's happening in example three. Find the power of a complex number? It says to put the base equation into standard form but then does not actually do that. It used the r= step though, and the tan angle step, but i still cant tell how to get the answer for the angle. Am i just an idiot and its just through using the unit circle? Again?
then after that its got z = r cis angle, then uses the power from the base equation like earlier. Multiples it against the angle and used it as a power for r. Oh, THEN it puts it into standard form?? Thats a lot of steps. I don't really understand what's happening there in the next few steps but it somehow gets simplified down to = yi
the next few examples are about square and cube rooting complex numbers. I can't even being to comprehend what's happening there
the review uses methods of solving some shit that wasnt even in the notes, so ive got no clue whats going on with that even though it is actually the exact types of problem as above. Weird
