Prove the basic properties of the norm of the Gaussian integers... | Filo
Prove the basic properties of the norm of the Gaussian integers... | Filo
May 17, 2025
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MathxMatrix on Instagram: "In the Gaussian integers (complex numbers of the form a + bi where a and b are integers), 2 is not prime. Why? Because it factors nontrivially: 2 = (1 + i)(1 - i) Here, both 1 + i and 1 - i are Gaussian integers, and neither is a unit (i.e., neither is ±1 or ±i). That means 2 can be broken down into smaller non-unit Gaussian integers—so it fails the definition of primality in that domain. Original video from the Yt channel #feephifofum"
MathxMatrix on Instagram: "In the Gaussian integers (complex numbers of the form a + bi where a and b are integers), 2 is not prime. Why? Because it factors nontrivially: 2 = (1 + i)(1 - i) Here, both 1 + i and 1 - i are Gaussian integers, and neither is a unit (i.e., neither is ±1 or ±i). That means 2 can be broken down into smaller non-unit Gaussian integers—so it fails the definition of primality in that domain. Original video from the Yt channel #feephifofum"
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