>>14027385Exponents mean roots. Square means you have two roots of identical length. You shrink and grow the roots identically to get the output, or power. Decimal exponents mean reverse. You have the power. You want the length of the roots. You break it up into (e^3i) * (e^~0.1415926i).
An imaginary is nothing to get tripped up over here. It just means a compound number e^3i = (A + Bi)(A + Bi), so (2AB)^-3 = e and A^2 = B^2, something along that it's not important. It's just possible to do.
e^x is a function who's output also the slope at x. You are rotating a fixed line segment:
| / - \ | / - \ |
e goes on forever. pi goes on forever. You can cancel out these two parts that go on forever with power vs. roots.
Imaginary numbers throw in a negative so precision settles and cancels out instead of accumulates.
