# Thread: Solve equation with e for "b"

1. ## Solve equation with e for "b"

Could anyone help me with the steps to solve this equation for b ?

2. ## Re: Solve equation with e for "b"

Originally Posted by rickS
Could anyone help me with the steps to solve this equation for b ?
$\exp( i\pi)=-1$
So you have $(\exp(\pi))^2+b^2=1$
Can you now find $b~?$

3. ## Re: Solve equation with e for "b"

Plato, that is helpful. But I am still a bit lost; what if it is an "x" instead of pi:

Such that we cannot use exp(ipi) = -1

4. ## Re: Solve equation with e for "b"

Originally Posted by rickS
Plato, that is helpful. But I am still a bit lost; what if it is an "x" instead of pi:

Such that we cannot use exp(ipi) = -1
@rickS, the new equation is $\large\left(e^{ix}\right)^2=\large\left(e^{x} \right)^2+b^2$, solve for $x$.
Now we have a very difficult problem. Whole courses a devoted to the study of theory of equations. And courses on numerical methods.

Here is a sample from the above: $\left(e^{ix}\right)^2=\left(e^{i(2x)}\right)=\cos (2x)+{\bf{i}} \sin(2x)$

I hope you can the difficulty solving for $x$ in: $\cos(2x)+{\bf{i}} \sin(2x)=e^{2x}+b^2~?$