Let C be the set of complex numbers Define addition on C by (a bi) (c di) (a c) (b d)i and define scalar multiplication by (a bi) a bi for all real numbers a Show that C is a vector space with these operations

Question: Let C be the set of complex numbers. Define addition on C by (a + bi) + (c + di) = (a + c) +

Let C be the set of complex numbers. Define addition on C by
(a + bi) + (c + di) = (a + c) + (b + d)i
and define scalar multiplication by
α(a + bi) = αa + αbi
for all real numbers a. Show that C is a vector space with these operations.

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