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Answer by Hagen von Eitzen for Comparing square roots of negative numbers

There is no order relation on $\mathbb C$ (that is compatible with addition and multiplication the way we "need" it).For example, the product of two negative or two positive numbers in an ordered field...

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Answer by Gerry Myerson for Comparing square roots of negative numbers

There is no consistent definition of "larger than" in the complex numbers. One can say that the modulus of $\sqrt{-11}$ is less than that of $\sqrt{-13}$.

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Comparing square roots of negative numbers

If we have for instance $\sqrt{-25}$, that is, a square root of $-25$, I know the answer can be $5i$ (Is $-5i$ also correct? Sorry not professional in mathematics).My main question here is how to...

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