I am studying the ring theory and I got some point like $(2+3i)$ divides $(-1+5i)$ in the Eucledian domain $\mathbb{Z}[i]$. I do not know that how it can be possible. Please let me know about this.
2025-01-13 03:07:33.1736737653
Division in $\mathbb{Z}[i]$
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Just do the division in $\mathbb{C}$: $$ \frac{-1+5i}{2+3i}=\frac{(-1+5i)(2-3i)}{4+9}=\frac{-2+10i+3i-15i^2}{13}=1+i $$ The quotient is in $\mathbb{Z}[i]$.
By the way, both $1+i$ and $2+3i$ are primes in $\mathbb{Z}[i]$.