Let R2x2 be the set of all 2x2 real matrices and consider function phi : C --> R2x2 given by phi(a+bi) :=  a -b b a for all a+bi element of C (1) Show that phi is one-to-one (2) Describe the range/image of phi. i.e. describe the set phi(C) = {phi(z)|z element of C} (3) Prove or disprove: phi(z1+z2)=phi(z1)+phi(z2), for all z1,z2 element of C (4) Prove or disprove: phi(z1 x z2)=phi(z1) x phi(z2), for all z1,z2 element of C

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