someone to help me with this
factorise 5550 fully in
1) the integers
2) the Gaussian integers?????????
I assume you can do 1).
For 2), you need to know that if p is an integer prime of the form 4k+3 then it is also a Gaussian prime. If it is of the form 4k+1 then it is always possible to express it as a sum of two squares, $\displaystyle p=a^2+b^2$. Then p factorises in the Gaussian integers as $\displaystyle p=(a+ib)(a-ib)$, and those factors are both Gaussian primes. Finally, 2 factorises in the same way, $\displaystyle 2=(1+i)(1-i)$.
So for example 11 is a Gaussian prime, but $\displaystyle 13 = 3^2+2^2 = (3+2i)(3-2i)$.