I am trying to find i−1. I already know that the answer is −i, but I can't figure out a way to determine that using math. This is what I am doing: i−1
1i
√(1i)2
√1−1
√−1
±i
What am I doing wrong?
Answer
I'm not sure where your 3rd expression comes from. In general, to find 1a+bi, where a,b∈R, multiply numerator and denominator by the conjugate ¯a+bi=a−bi to obtain 1a+bi=a−bi(a+bi)(a−bi)=a−bia2+b2
In your case, take a=0,b=1 to obtain 1i=−1i1=−i.
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