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I've set up this equation to find the integral time in a PI-regulator.

[tex] \frac{\sqrt{0.02^2 - 4 \times \frac{0.02}{X}}}{2} = \frac{\pi}{100} [/tex]

This is not solvable by normal means because the X has to be postive, thus rendering the square root negative.

I have tried by substistuting values for X, and found that if X = approx. 18,4 it will all add up.

The problem is that when solving this equation the "normal" way, it will no longer be complex when squaring the root. The answer results in approx -22.54.

What do I have to do to solve this equation and get an exact answer for X in the imaginary plane?

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# Complex equation

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