How is a complex number a group under addition.
How is a complex number a group under multiplication(without zero)
How is a complex number a group under addition.
How is a complex number a group under multiplication(without zero)
A complex number is not a group under addition. The set of all complex numbers is a group under addition. Just look at the definition of a group and see that you can verify the axioms. Similarly for the set of complex numbers without zero and multiplication.