If \(\displaystyle m=\mp k\cdot i\) where \(\displaystyle k\in \mathbb R\)* and \(\displaystyle i^2=-1\) , then does the equation have solutions? If yes, then what are the solutions of the equation?
Thank you very much!

If \(\displaystyle m=\mp k\cdot i\) where \(\displaystyle k\in \mathbb R\)* and \(\displaystyle i^2=-1\) , then does the equation have solutions? If yes, then what are the solutions of the equation?
Thank you very much!

The right-hand side must be real.
There are no solutions if the right-hand side is less than 2.
If the right-hand side equals 2, $x = 1$ is the unique real solution.
If the right-hand side exceeds 2, there are two real solutions (that are easily found, but you didn't find them).

If \(\displaystyle m=\mp k\cdot i\) where \(\displaystyle k\in \mathbb R\)* and \(\displaystyle i^2=-1\) , then the equation becomes \(\displaystyle |x-2|+|x-1|+|x|=k^2\) and so what are the solutions of the initial equation?Thank you very much!

What are the solutions of the initial equation \(\displaystyle |x-2|+|x-1|+|x|=-m^2\) where \(\displaystyle m\) is a some parameter?Thank you very much!