i3=iii=√−1√−1√−1=√(−1)(−1)(−1)=√−1=i
Please take a look at the equation above. What am I doing wrong to understand i3=i, not −i?
Answer
We cannot say that √a√b=√ab for negative a and b. If this were true, then 1=√1=√(−1)⋅(−1)=√−1√−1=i⋅i=−1. Since this is false, we have to say that √a√b≠√ab in general when we extend it to accept negative numbers.
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