/sci/ - Science & Math

>>11602115
>Answer is: the same way you did. Since it describes a position on the circle, adding angles must lead to the same result as doing two rotations about the summands
Can you write out the proof if full? I honestly have no idea what you mean.
>>11602116
>But it looks like a definition to me. If I prove it by saying it is the definition, surely you will accuse me of being circular.
You can use it as a definition, but then you cannot use the property that e^(ix) * e^(iy) = e^(i(x+y))
>Have you got another identity to offer as a definition of e^(ix) where x is real?
Sure, the common mathematical definition is
e^ix = 1 + ix + (ix)^2/2 + (ix)^3 / 6 + ....
>>11602117
I can see a way to prove it using it. But first you would need to calculate the derivatives of sin and cos. How would you do it?
>>11602125
What?