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x=\frac{1}{i}
Divide both sides by i.
x=\frac{i}{1i^{2}}
Multiply both numerator and denominator of \frac{1}{i} by imaginary unit i.
x=\frac{i}{-1}
By definition, i^{2} is -1. Calculate the denominator.
x=-i
Divide i by -1 to get -i.