GRE Exam Programming Functions

Suppose f is an analytic function of the complex variable z = x + i y given by
f(z) = (2x + 3y) + i g (x, y)
where g(x, y) is a real-valued function of the real variables x and y. If g(2, 3) = 1, then g(7, 3) = ?
(A) -14
(B)-9
(C) 0
(D) 11
(E) 18

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GRE Other Question

Suppose A and B are n*n invertible matrices, where n >1, and I is the n*n identity matrix. If A and B are similar matrices, which of the following statements must be true?
I. A - 2I and B – 2I are similar matrices.
II. A and B have the same trace.
III. A^-1 and B^-1 are similar matrices.
(A) I only
(B) II only
(C) III only
(D) I and III only
(E) I, II, and III
The group of symmetries of the regular pentagram is isomorphic to the
(A) symmetric group S5
(B) alternating group A5
(C) cyclic group of order 5
(D) cyclic group of order 10
(E) dihedral group of order 10