| Draw a Venn diagram of sets A, B and C where A ⊆ B, A ∩ C ≠ φ, B ∩ C = φ . |
| What is the universal set you have chosen? Justify your choice of sets in the diagram. |
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Find the polynomial over R of least degree which has i − 3 and
sqrt(7) + 5i as its roots.Prove that 
Obtain the polar and exponential representations of z1 , z2 and z1z 2 , where zi = 1/2 - 2i and z2 = 3 + i
Is Cramer’s Rule applicable for solving the linear system below? If yes, apply it.
Otherwise, alter the last equation in the system so that the solution can be obtained
by applying the Rule.
x + y + z = π
− πx + πy +sqrt(2z) = 0
π2 x + π2 y + 2z = 0 .
Find the roots of the equation 2x3- x2 − 22x − 24 = 0 , if two of them are in the ratio 3 : 4 .
Solve by substitution, the system you have obtained in 5(a) .
Apply De Moivre’s theorem to write (sqrt(3 + 1)5 in the form a + ib , with a, b ∈ R