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Problem 3. Suppose a and b are both non zero real numbers. Find realnumbers c and d such that1a + ib= c + id:Problem 4. Find all values of 2 C such that 1 + i; 2 i= 2 + 2i; 2 i.Problem 5. Suppose v;w 2 V . Explain why there exists a unique x 2 V suchthat v + 3x = w.Problem 6. Let 1 and 1 denote two distinct objects, neither of whichis in R. De ne an addition and scalar multiplication on R[f1g [ f1g.Speci cally, the sum and product of two real numbers is as usual, and for t 2 Rde net1 =8:1 if t 00 if t = 01 if t 0;t 1 =8:1 if t 00 if t = 01 if t 0;t +1 = 1+ t = 1; t + 1 = 1+ t = 1;1+1 = 1; 1 + 1 = 1; 1+ 1 = 0:Determine whether R[f1g [ f1g is a vector space over R