Why is |sqrt(i)| = 1? (Imaginary Unit Explanation)

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The discussion clarifies why the absolute value of the square root of the imaginary unit, |sqrt(i)|, equals 1. Participants emphasize the importance of recognizing that in the norm formula, the imaginary part of the complex number is crucial. The norm can also be calculated by explicitly determining i^{1/2} and confirming that the result is consistent. This understanding is essential for accurately working with complex numbers in mathematical contexts.

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  • Knowledge of the imaginary unit (i) and its significance
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Why is |sqrt(i)| = 1? (where i is the imaginary unit)

I thought to find a norm you do sqrt(x^2 + y^2) so isn't it
sqrt(0 + sqrt(i)^2)
= sqrt(i)

??

What am I doing wrong here?

nvm, i got it...
 
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For anyone else reading this and curious about a similar issue, it is important that you recognize that y in the formula for the norm is simply the imaginary part of the complex number (which is real, of course).

Of course, the other way to calculate the norm is to explicitly find i^{1/2} and find the norm of this. You will find that it is the same.
 

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