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

  1. #1
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    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.
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  2. #2
    MHF Contributor chiph588@'s Avatar
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     \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?
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