Factor into primes (=irreducibles): $\ 2+25\sqrt{-1} \in \mathbb{Z} [\sqrt{-1}] $?

Question

How can I factor below into primes, thank you!

$\ 2+25\sqrt{-1} \in \mathbb{Z} [\sqrt{-1}] $

Answer 1

Note that the square of the modulus of $2+25i$ is $2^2+25^2=629= 17 \times 37$. Now \begin{eqnarray*} 2+25i=(a+bi)(c+di) \end{eqnarray*} where $a^2+b^2=17$ and $c^2+d^2=37$ ... can you get values for $a,b,c,d$ that work ?

$(1+4i)(6+i)$.