In 9th grade I had an argument with my teacher that
i3=i
where i=√−1
But my teacher insisted (as is the accepted case) that:
i3=−i
My Solution:
i3=(√−1)3
i3=√(−1)3
i3=√−1×−1×−1
i3=√−1
i3=i
Generally accepted solution:
i3=(√−1)3
i3=√−1×√−1×√−1
i3=−√−1
i3=−i
What is so wrong with my approach? Is it not logical?
I am using the positive square root. There seems to be something about the order in which the power should be raised? There must be a logical reason, and I need help understanding it.
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