[BUG ?] Who can explain to me the CAS options "Use i" and "complex"?

[dg1969]

More precisely my question is: Why this wrong answer rather an answer like "no real solution" ?

If "Use i" and "Complex" are not checked that assumes (that's what I imagine) that \(z\) is real.

And of course if \( z\in \mathbb{R}\) then \(\bar{z}=z\)... The "wrong solution": \( \frac{1}{4+i}\) is in fact the only complex solution that satisfy this other equation::

\( (3+2i)z+(1-i)z-1=0 \)

In my mind if the options "Use i" and "Complex" ( I assume \( z \in \mathbb{R}\) )are not checked then with my initial equation the cZeros() function should answer "No solution" or else the system should display an alert indicating that the options need to be modified for a complex response to be provided.

For me there is a problem. Because I was looking for a complex solution. The calculator gives me a bad one and I may not realize it ...