problem with solving one complex number problem

Question

Is $1= -1$ ?
because, $1=\sqrt{1} =\sqrt{-1×-1} =\sqrt{-1}×\sqrt{-1 } = i×i = i^2 = -1 $
this can be done with all natural numbers. how this can be? please help me

Answer 1

On complex number this step is wrong

$$1=\sqrt{1}$$

since $\sqrt{1}=(e^{2\pi i})^{\frac12}\pm 1$ and also this one

$$\sqrt{-1}=i$$

since $\sqrt{-1}=(e^{\pi i})^{\frac12}=\pm i$.