How does complex impedance measurement determine voltage transformer VT ratio (2500:1)?

I need some help to understand the theory behind a test in a voltage transformer. Here is the thing:
Recently I performed a test in a voltage transformer in order to check its turn ratio and we did such task with the aid of a proper instrument and a respective application note. The VT rated voltage is 500 kV and turn ratio is 2500:1.
According to the note the proccedure is the following (image below):
1 - Measure the complex impedance of a capacitor / resistor (Z1);
2 - Measure the complex impedance of the previous capacitor in series to the voltage transformer under test (Z2).
According to the note the VT Ratio and the VT phase angle is:
VT ratio =  Z2/ Z1and VT phase angle = θ2−θ1
In this case the VT ratio was = 2494.795152 and the VT phase angle = -0,0664. You can see the details of the circuit down bellow.
The point is: I can't understand the theory behind this test. How is the total complexe impedance related to the VT ratio? In the following links there is a question about using a transformer as an inductor (which is the configuration of the second circuit in our measurement). What is, mathematically speaking, the relation between the complexs impedances and the VT ratio?

Voltage transformer
Transformer as an inductor

Those are the links I mentioned.

Hi Sergio,
Generally the test equipment used to carry out these tests work by 2 different but related methods. They either test the CT or VT using an injected current or an injected voltage. Then calculate the ratios of the windings based on the resistances measured. Simply ohms law.  And give you a ratio deviation based on the expected ratio that you can verify according to the manufactured standard. Normally the more advanced test equipment will ask for in a drop down menu which standard it is being tested to and can give you a pass fail output.
There is nothing particularly mathematical about this test. I hope this helps.

Thanks for replying.
Indeed, most of the tests that we perform using this test set are pretty automatic. However, specifically in the case of measuring VT ratio, the situation is different. For example, we have to calculate by ourselves the VT ratio and the phase angle as shown above. The proccedure works quite well, once again, my question is related to the theory behind it.I thought that maybe this relation between impedance and turn ratio are related to each other according to the following expression: Z1 = a2 . Z2 -> (Z1 = Impedance of primary side, Z2 = Impedance of primary side and a = rated turn ratio). But it's still not clear for me how i could use this expression, since in the second measurement the transformer becomes a huge inductor.
In this link you can check the application note.
VT ratio

Hi the impedance to turns ratio formula is given as the sqrt(Np/Ns) = sqrt(Z2/Z1) if you plug in the results that you got you should see that they are very nearly equal. They will not be exact obviously.

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