Let $S$ be the set of complex numbers of the form $a + bi,$ where $a$ and $b$ are integers.  We say that $z \in S$ is a unit if there exists a $w \in S$ such that $zw = 1.$  Find the number of units in $S.$
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Let $S$ be the set of complex numbers of the form $a + bi,$ where $a$ and $b$ are integers.  We say that $z \in S$ is a unit if there exists a $w \in S$ such that $zw = 1.$  Find the number of units in $S.$
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Let $S$ be the set of complex numbers of the form $a + bi,$ where $a$ and $b$ are integers.  We say that $z \in S$ is a unit if there exists a $w \in S$ such that $zw = 1.$  Find the number of units in $S.$
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