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This equation is based on the Sine function

Let w = 2 Pi f

The basic V I equation for an inductor is

V(t) = L d/dt I(t)

Now

I(t) = A Sin(w t)

V(t) = L d/dt I(t)

V(t) = L A w Cos(w t)

Z = Vrms / Irms

Now

Vrms = A L w /Sqrt(2)

Irms = A/Sqrt(2)

Therefore

Z = Vrms / Irms

( A L w /Sqrt(2))

-----------------------

( A/Sqrt(2) )

Equals

L w

L 2 Pi f

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