Prove or disprove the statements: (a) If x is a real number suchthat |x + 2| + |x| ? 1, then x 2 + 2x ? 1 ? 2.
(b) If x is a real number such that |x + 2| + |x| ? 2, then x 2+ 2x ? 1 ? 2.
(c) If x is a real number such that |x + 2| + |x| ? 3, then x 2+ 2x ? 1 ? 2.
(d) If x is a real number such that |x + 2| + |x| ? 5, then x 2+ 2x ? 1 ? 2.
(2) Prove or disprove the statements: (a) If z is a complexnumber such that |z + 1| + |z ? 1| ? 3, then |z 2 ? 1| ? 2.
(b) If z is a complex number such that if |z 2 ? 1| ? 2, then |z+ 1| + |z ? 1| ? 3.
(3) A clock with a face that has the numbers 1 through 12 hasthree hands that indicate the second, minute and hour of theday.
Assume that the center of the clock is at position (0, 0), andat noon the end points of the hands are (respectively) at (0, 1),(0, 3/4), (0, 1/2).
(a) Give the position of the end points of each of the hands attime t where t represents the number of seconds after noon in bothpolar and rectangular coordinates (make sure that you label whichyou are using clearly).
(b) At what times do your equations say that the hands of theclock will all align?
