Absolutely, Norm!

The norm of a Gaussian integer is 100.

What is its absolute value?


The answer is 10.

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2 solutions

Geoff Pilling
Jan 20, 2017

If z = a + b i z = a + bi , then the norm is given by:

N ( z ) = a 2 + b 2 N(z) = a^2 + b^2

And the absolute value is given by:

z = a 2 + b 2 = N ( z ) = 100 = 10 |z| = \sqrt{a^2 + b^2} = \sqrt{N(z)} = \sqrt{100} = \boxed{10}

Samuel Erens
Feb 3, 2020

The norm of a Gaussian integer is defined as the square of the absolute value. Therefore, the absolute value of a Gaussian integer is the square root of the absolute value. Therefore, if the norm of a Gaussian integer is 100, the absolute value is the square root of 100, which is 10.

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