154 questions linked to/from Why $\sqrt{-1 \cdot {-1}} \neq \sqrt{-1}^2$?
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### Why is $i^3$ (the complex number "$i$") equal to $-i$ instead of $i$? [duplicate]

$$i^3=iii=\sqrt{-1}\sqrt{-1}\sqrt{-1}=\sqrt{(-1)(-1)(-1)}=\sqrt{-1}=i$$ Please take a look at the equation above. What am I doing wrong to understand $i^3 = i$, not $-i$?
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### Why $\sqrt{-1 \times -1} \neq \sqrt{-1}^2$? [duplicate]

We know $$i^2=-1$$then why does this happen? $$i^2 = \sqrt{-1}\times\sqrt{-1}$$ $$=\sqrt{-1\times-1}$$ $$=\sqrt{1}$$ $$= 1$$ EDIT: I see this has been dealt with before but at least with ...
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### What is $\sqrt{-4}\sqrt{-9}$? [duplicate]

I assumed that since $a^c \cdot b^c = (ab)^{c}$, then something like $\sqrt{-4} \cdot \sqrt{-9}$ would be $\sqrt{-4 \cdot -9} = \sqrt{36} = \pm 6$ but according to Wolfram Alpha, it's $-6$?
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### What's wrong with this proof $1=i^2=-1$ [duplicate]

I just thinking what $i^{i}$ should be, arrived at a quiet awkward thing. So this was that awkward thinking : Let $i^{i} = a$ $(i^{i})^{2i} = a^{2i}$ $i^{-2}=a^{2i}$ $-1=a^{2i}$ Now if we take power ...
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### Is $i$ equal to $-i$? [duplicate]

When I was in high school, I learned about $i$ in math class and I remember asking my teacher back then if $i$ was equal to $-i$ according to the simple following development : \begin{equation} i=\...
### imaginary number $i$ equals $-6/3.4641$? [duplicate]
$$-4^3 = -64$$ so the third root of $-64$ should be $-4$ than. $$\sqrt{-64} = -4$$ But if you calculate the third root of -64 with WolframAlpha( http://www.wolframalpha.com/input/?i=third+root+of+-...