-1i + { 2i / [ [(e^(-2i*atan(x))^1i]^1i + 1 ] } = x . Find x ? . How many solutions ?

[lvl107]

Hello, Everyone.

Thanks in advance for your time and help.

Regards.

[MatthewHawkins]

I cant view your attachment because i dont have mathcad but, I believe the answer is four real and four imaginary. Sorry if this was not what you needed help with.

[Werner_E]

Its the identity again (at least from Mathcad's point of view).

Are you trying to tease us?

[MatthewHawkins]

No sorry, i thought you just wanted the solutions to the equation which are:

x = -0.145819 + 0.940201i

x = -0.00779584 + 1.01064i

x = 0.00779584 + 1.01064i

x = 0.145819 + 0.940201i

,guess i was wrong.

[LucMeekes]

Matthew,

Werner was replying to Loi Le..

Anyway, there are much more solutions.

[Werner_E]

Confusion! I am not the OP and I didn't reply to your post.

My reply was to LoiLe's initial post. The LHS of his equation can be simplified to x (at least if you ignore the fact that we have a lot of ambiguities here and the LHS in fact simplifies to an infinite numer of results). And so he is trying to find solution for the identity x=x.

Its not the first time LoiLe is posting that kind of question and he was informed a couple of times abou the various ambiguities when you deal with complex numbers and also about the limitations of Mathcad's symbolic (which can't simplify the LHS to x without a little help.

The remark about teasing us was meant tongue in cheek as I guess the real issue is a language problem.

This is the step Mathcad is not capable of

Then the simplification is no problem

and probably Mathcad is here using the conversion

BTW, how did you arrived at your solutions?