In class while messing with fractions and complex numbers I found this "paradox" $$ \sqrt{-1}=\sqrt{-1} $$ $$ \sqrt{\frac{-1}{1}}=\sqrt{\frac{1}{-1}} $$ $$ \frac{\sqrt{-1}}{\sqrt{1}}=\frac{\sqrt{1}}{\sqrt{-1}} $$ $$ \sqrt{-1}\cdot \sqrt{-1}=\sqrt{1}\cdot \sqrt{1} $$ $$ i\cdot i=\sqrt1 $$ $$ -1=1 $$ Could anybody explain me what is wrong with this passages?
2025-01-13 00:04:18.1736726658
Strange problem with the imaginary unit
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