Problem statement:
Find a generator of the ideal $(85, 1+13i)$ in $\mathbb{Z}[i]$, i.e., a GCD for $85$ and $1 + 13i$ by the Euclidean Algorithm. Do the same for the ideal $(47-13i, 53+56i).$
Can you please outline the steps, then I can practice with others.
Source: Abstract Algebra by Dummit & Foote, $\S$8.1 #7