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\[\mathbb{Z}[i]=\{a+bi\;|\;a,b\in\mathbb{Z}\} \quad\text{and}\quad i=\sqrt{-1}\]

That's what I thought, but just wanted to verify.

I must go, but I will think about this.

And I'm too anally autistic to not correct it :)

Haha, I'll re-type it later, I guess...

Just fyi for people reading, how I thought the modular arithmetic worked at first, was not correct.