Solving sqrt(i)=z, one or two solutions?

[sasa]

Another interesting example...

Solve: \( \sqrt{i} = z \)

Not at all complicated task, it have two solutions. However, we will get interesting results from the Prime, depending how we formulate it for solving.

Let try first simply \( \sqrt{i} \), it returns \( \frac{1+i}{\sqrt{2}} \)
Let try further solve((sqrt(i)) = z,z), result is \( \left \{ \frac{1+i}{\sqrt{2}} \right \} \)
However: solve((i) = (z^2),z), result is \( \left \{ \frac{1+i}{\sqrt{2}}, -{\frac{1+i}{\sqrt{2}}} \right \} \)

An obvious path for lower grade students to solve it, is to use elementary definition of a complex number. Another solution can be using Euler's formula...

However, the Prime unexpectedly gave different number of solutions, depending on how formula is written...

Disclaimer: Tested on latest public beta emulator only.