6 ms·
I was taught that Eulers formula defined complex exponents? If we used turns for cos and sin we could redefine what e^ix means so it works without radians. Fro
by dosshell 4y ago
I was taught that Eulers formula defined complex exponents?
If we used turns for cos and sin we could redefine what e^ix means so it works without radians. From the other answer I guess this is completely wrong...
(I do understand it is nuts to redefine, i'm just interested as a theoretical thought)
Now, how is Eulers formula is deduced? How did we figure out what e^ix means?
- johnbcoughlin 4y agoOne way to understand where the formulas come from is the power series of e^x, remembering that that function is (can be) defined as the function whose derivative is itself. Sin and cos are functions whose second derivative is -sin and -cos respectively. If you plug in ix to the power series for e^x, the complex exponential comes right out. There are a couple other "paths" to this result, and the choice we have is by far the most elegant.