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 α. Show that C is a vector space with these operations.
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 α. Show that C is a vector space with these operations.