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The square root of a positive real number can either be +/-. The principle square root is defined as the positive value. sqrt(9) is +/- 3, but the principle square root of 9 is 3.

For complex numbers the principle square root is the argument (or angle) of the complex number that lies between (-pi,pi]. I am pretty sure that the upper angle pi is closed while the lower angle -pi is open, but not 100%.

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Q: Definition of principle square root
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