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# GCD of gaussian integers watch

1. I'm trying to follow this example (which uses the euclidean algorithm):

Compute a greatest common divisor of and .

. The quotient in is

so we take the quotient to be .

I don't really understand this. Can someone explain how is computed?
2. (Original post by notnek)
I'm trying to follow this example (which uses the euclidean algorithm):

Compute a greatest common divisor of and .

. The quotient in is

so we take the quotient to be .

I don't really understand this. Can someone explain how is computed?
My guess is that in this step they're seperating k1 and p, getting

So, k is the non fractional part, so 4i.
3. (Original post by Slumpy)
My guess is that in this step they're seperating k1 and p, getting

So, k is the non fractional part, so 4i.
But

Why not ?

I think this may have something to do with a lattice of squares which can compare two gaussian integers but I'm not sure.
4. You want the "remainder" to be as small as possible, and (16+138i) is a lot larger than (16-55i).
5. (Original post by DFranklin)
You want the "remainder" to be as small as possible, and (16+138i) is a lot larger than (16-55i).
OK but if I only have , how do I find because it could be anything. In another example I have, it's .

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