The set C of all complex numbers, with the usual operations of addition and real scalar multiplication, forms a vector space. Elements of C can be written in the form æ + iy, where i is the imaginary unit. 1. Show that closure is satisfied for C under addition and scalar multiplication. What is the zero "vector" in this vector space? 2. Come up with two different subspaces of C other than (0} and C itself. Explain how they satisfy the definition of a subspace. 3. R is closed under multiplication; in other words, the product of two elements Ris also in R. Can we say the same for C? Why or why not?

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