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

1. ## 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.

2. $\frac{a+bi}{1+i} = \frac{a+b}{2} - \left(\frac a2 - \frac b2\right)i$ 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?