Question 1 (7 marks) Consider the sets
C = {(x, y) ∈ R2 | x2 − y2 = 1}
P = { 1/2 ( e t + e − t ) i + 12 ( e t − e − t ) j | t ∈ R }

(a)  Prove carefully that P ⊆ C.

(b)  Is it true that C ⊆ P ? If your answer is yes, prove it. If your answer is no, give a specific element(x,y)∈C\P andexplainwhy(x,y)∈/P.


Question 2 (10 marks)
(a) For the complex numbers
z1=2− √ 3i, z2= √ 2e 4 , z3= √ 3−i:
(i) Express z1z3 in Cartesian form.
(ii) Calculate |z2| +