# Math Help - Euler Formula..

1. ## Euler Formula..

Suppose you want to solve $\cos x + i \sin x = \text{cosh}(y-1) + ixy$.

Without resorting to graphs could we do the following: $e^{ix} = \frac{e^{y-1}+e^{1-y}}{2} + ixy$?

2. Originally Posted by manjohn12
Suppose you want to solve $\cos x + i \sin x = \text{cosh}(y-1) + ixy$.

Without resorting to graphs could we do the following: $e^{ix} = \frac{e^{y-1}+e^{1-y}}{2} + ixy$?
Yes
But I don't think it's possible to solve it easily oO
And maybe it's better to identify real and imaginary parts :

cosh(y-1) is a real number. So cosh(y-1)=cos(x)
and xy=sin(x)

3. So we have two cases: $x=0, \ x \neq 0$.