IGNOU MTE 6 2026 - Check whether or not is a subgroup ofi) , &nb

Question

Check whether or not $A = \{z \in \mathbb{C}^ \mid |z| \in \mathbb{Q}\}$ is a subgroup of

i) $(\mathbb{C}^, \cdot)$ , $\quad \quad$ ii) $(\mathbb{C}, +)$

09 Jan 2026

Answer :

Word Count : 103

Consider (A={z\in\mathbb{C}^* \mid |z|\in\mathbb{Q}}). For ((\mathbb{C}^*,\cdot)): The set (A) is nonempty since (1\in A) and (|1|=1\in\mathbb{Q}). If (z,w\in A), then (|z|,|w|\in\mathbb{Q}), and (|zw|=|z||w|\in\mathbb{Q}), so (zw\in A); hence (A) is closed under multiplication. For

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