Find an onto homomorphism from the additive group $\mathbb{C}$ of complex numbers to the multiplicative group $\mathbb{C}^*$. Justify and find its kernel.
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there is no multiplicative group of all complex numbers.... – Bhaskar Vashishth Sep 25 '15 at 18:16
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I think he meant ($\mathbb{C}$ \ {0} , *) – Sep 25 '15 at 18:18
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Hint: Maybe it is easier for you to solve this over $\mathbb R$ rather than $\mathbb C$. – air Sep 25 '15 at 18:27
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@ Bhaskar Are u sure?? Since my professor asked me in the assignment... – Pranay Reddy Sep 25 '15 at 18:36
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Pranay, see Vader's comment to understand Bhaskar's. – anon Sep 26 '15 at 04:26
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Hint: find a function such that $f(x+y) = f(x)f(y)$. – zhoraster Sep 26 '15 at 05:11