# abstract algebra question concerning groups

Are these groups? If so show it, and if not provide a counterexample.

The set of all complex numbers $x$ that have absolute value $1$, with operation multiplication. Recall that the absolute value of a complex number $x$ written in the form $x = a +bi$, with $a$ and $b$ real, is given by $|x| = |a+bi| = (a^2 + b^2)^{1/2}$.

The set of all complex numbers $x$ that have absolute value $1$, with operation addition.

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As I mentioned on your earlier question, it is not considered polite here to tell other users to do something. Your question does not show that you have thought about the problem. Please explain what you've tried so far, and where you are stuck. –  Zev Chonoles Apr 8 '12 at 23:47
The properties of a group are 1) closure, 2) identity, and 3) inverse. Have you tested these cases against these properties? Where are you stuck? –  Tpofofn Apr 9 '12 at 0:03

Hint: for $z,w\in\mathbb{C}$, $|zw|=|z||w|$ but $|z+w|\leq|z|+|w|$.