I have this problem following.
Two elements $a$ and $b$ of a commutative ring $\mathbb{R}$ with one are said to be associated if there is a unit $u$ in $\mathbb{R}$ such that $a = u \cdot b$
Find $a \in \mathbb{Z}$ such that $87 + 13i$ and $13 + ai$ are associated in $\mathbb{Z}[i]$.
I thought this as set these equal:
$87+13i=u \cdot (13+ai)$ and i thought you could set u to i? $87+13i=i \cdot (13+ai) \implies 13i-a = 87+13i$ do i thinking correct but the answers when i check them says $a=-87$ and $u=-i$ i'dont understand how to solve it?