# In Z[i], show that 1+i divides...

• Apr 21st 2010, 03:29 PM
NikoBellic
In Z[i], show that 1+i divides...
In Z[i], show that 1+i divides a+bi precisely when a is congruent to b mod 2.
• Apr 21st 2010, 03:37 PM
chiph588@
$\frac{a+bi}{1+i} = \frac{a+b}{2} - \left(\frac a2 - \frac b2\right)i$ since $\frac{1}{1+i} = \frac{1-i}{2}$.

So we need $a+b$ and $a-b$ to be even. What does this tell us?