31.1  a) ExpToTrig[e^(i*0)]
      b) ExpToTrig[4*e^(i*pi/6)]
      c) ExpToTrig[8*e^(i*7*pi/6)]
      d) ExpToTrig[3*e^(i*(pi*(-5/2)))]

31.2  a) ExpToTrig[e^(i*(pi*(-1/2)))]
      c) ExpToTrig[e^(-i)]
      d) ExpToTrig[2*e^(i*(pi*(1/3)))]
      e) ExpToTrig[e^(i*(pi*(1/4)))-e^(i*(pi*(-1/4)))]
      f) ExpToTrig[2*e^(i*(pi*(1/4)))/(e^(i*(pi*(-3/4))))]
      h) ExpToTrig[(e^(i)-e^(-i))/(e^i+e^(-i))]

31.4  a) 4*e^(i*(pi*5/6))*(2*e^(i*(pi*1/3)))
         ExpToTrig[8*e^(i*pi*(7/6))
         4*e^(i*(pi*5/6))/(2*e^(i*(pi*1/3)))
         ExpToTrig[2*e^(i*pi/2)]

31.5  b) (((5+3i)*(5-3i))/(sqrt(2)(cos(5*pi/4)+i*sin(5*pi/4))))
      c) simplify (((1+i)^2)/(2(cos(pi*2/3)+i*sin(pi*2/3))))

31.7  expand (x-(2+i))*(x-(2-i))

31.8  (1-sqrt(3)i)^2-2*(1-sqrt(3)i)+4

31.12 (2+i)*(sqrt(2)/2+sqrt(2)/2*i)*(1/sqrt(2))
      (2+i)*(sqrt(2)/2-sqrt(2)/2*i)*(1/sqrt(2))