[Brilliant Blog] Gaussian Integers

Main post link -> http://blog.brilliant.org/2013/02/19/gaussian-integers/

Read the rest over at the blog. Feel free to share your thoughts or ask questions here.

Show that $1,\ -1,\ i,$ and $-i$ are Gaussian units and there are no other Gaussian units.

Find two Gaussian integers that have the same norm and are NOT multiplies of each other, hence the converse of the Example 2 is not true.

Show that $1+i$ is a prime. Hint: Norm.

4*. Show that every prime integer of the form $4k+3$ is also a Gaussian prime.

Easy Math Editor

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Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$