Plotting the equation $x - {(\cos(x) + i\sin(x))^{ix}} = 0$ I would like to plot this function:
$$x - {(\cos(x) + i\sin(x))^{ix}} = 0$$
I remember about $\cos(x) + i\sin(x) = e^{ix}$, so this can be written as $$x - {(e^{ix})^{ix}} = 0$$
or maybe better
$$x - {e^{ixix}} = 0$$
I know it's not that hard, but my math background is very rusty. I tried with wolfram, but I'm not sure why it's not plotting it. Maybe for the $i$?
Is there another tool I can use?

$$x - {(\cos(x) + i\sin(x))^{ix}} = 0\Longleftrightarrow$$
$$x - {(e^{ix})^{ix}} = 0\Longleftrightarrow$$
$$x - e^{ixix} = 0\Longleftrightarrow$$
$$x - e^{(ix)^2} = 0\Longleftrightarrow$$
$$x - e^{i^2x^2} = 0\Longleftrightarrow$$
$$x - e^{-x^2} = 0\Longleftrightarrow$$
(because $x$ is real we can write)
$$e^{x^2}x= 1\Longleftrightarrow$$
$$e^{x^2}= \frac{1}{x}\Longleftrightarrow$$
$$x^2=\frac{\log_{10}(\frac{1}{x})}{\log_{10}(e)}\Longleftrightarrow$$
$$x^2=\frac{\log_{10}(\frac{1}{x})}{\frac{1}{\ln(10)}}\Longleftrightarrow$$
$$x^2=\ln\left(\frac{1}{x}\right)\Longleftrightarrow$$
$$x^2=-\ln(x)\Longleftrightarrow$$
$$x=e^{-\frac{W(2)}{2}}=\sqrt{\frac{W(2)}{2}}$$

$W(x)$ is the Lambert $W$-function
