1. ## Simple equation problem

2. $\displaystyle y^2$ cannot be a negative number.
therefore the answer is $\displaystyle \oslash$

$\displaystyle y^2 = -\frac{1}{4}$
$\displaystyle y = \sqrt{-\frac{1}{4}}$
$\displaystyle y = ERROR$

and thus as vonflex1 said: $\displaystyle y^2$ can't be negative

4. ## there is an imaginary answer

$\displaystyle y = \frac{\sqrt{-1}}{\sqrt{4}} = \frac{i}{2}$

5. Ok,this simple equation is part of bigger complex numbers task:

and general solution for this task is:

than solution for must be in order to match general solution of this task?

6. not sure how that works?
$\displaystyle \left(-\frac{1}{2}\right)^2 \ne -\frac{1}{4}$

but

$\displaystyle \left(-\frac{i}{2}\right)^2 = -\frac{1}{4}$

7. Try to solve entire problem,than you will get to the part where

and I just don't know how solution of the task is ???

Ok,I agree about x value,but how did they get that y value? ???

Try to solve entire problem,than you will get to the part where

and I just don't know how solution of the task is ???

Ok,I agree about x value,but how did they get that y value? ???
Your original relation can be written as $\displaystyle |z| = |z + 1|$ and this defines a line (the perpendicular bisector of the line segment joining z = 0 and z = -1). If you substitute z = x + iy the same answer is easily got.

I have no idea where all your other stuff has come from since you refuse to show any of your working.

9. $\displaystyle |Z|=-\frac{1}{2}+ki$

$\displaystyle |Z+1|=\frac{1}{2}+ki$

$\displaystyle |Z|=\sqrt{(-0.5)^2+k^2}=\sqrt{\frac{1}{4}+k^2}$

$\displaystyle |Z+1|=\sqrt{(0.5)^2+k^2}=\sqrt{\frac{1}{4}+k^2}$