What fallacy is there?? [duplicate]

Please tell what is wrong with following :

$\iota=\sqrt{-1}$

multiply both sides with $\iota$

$\iota\cdot \iota=\sqrt{-1}\cdot\sqrt{-1}\Rightarrow\iota^{2}=\sqrt{(-1)\cdot(-1)}$

$\Rightarrow \iota^{2}=1$

which is ofcourse a contradiction. I know step

$\sqrt{-1}\cdot \sqrt{-1}=\sqrt{(-1)\cdot(-1)}$

is wrong but how to explain this to students who have just started learning complex numbers??

marked as duplicate by Moya, YoTengoUnLCD, Zev Chonoles, carmichael561, ThéophileMay 11 '16 at 4:26

The problem is that the symbol "$\sqrt{\cdot}$" does not have the clear-cut meaning with complex numbers that it has with positive real numbers. For positive reals, you always select the positive root. No such option exists in general with complex numbers, so the familiar rule $$\sqrt{a\cdot b}=\sqrt{a}\cdot\sqrt{b}$$ needn't hold.