5.1   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)))]

5.2   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))]

5.3   b) ExpToTrig[Abs(z)*e^Arg(z)] where z = 6i
      c) ExpToTrig[Abs(z)*e^Arg(z)] where z = 1+i
      d) ExpToTrig[Abs(z)*e^Arg(z)] where z = -1-i
      e) ExpToTrig[Abs(z)*e^Arg(z)] where z = -sqrt(3)+i
      f) ExpToTrig[Abs(z)*e^Arg(z)] where z = -3-sqrt(3)*i
      h) ExpToTrig[Abs(z)*e^Arg(z)] where z = -1/2+sqrt(3)/2*i
      i) ExpToTrig[Abs(z)*e^Arg(z)] where z = 7-2*i
      j) ExpToTrig[Abs(z)*e^Arg(z)] where z = 1.8+0.52*i
      k) ExpToTrig[Abs(z)*e^Arg(z)] where z = 6-6*sqrt(3)*i
      l) ExpToTrig[Abs(z)*e^Arg(z)] where z = 6+6*sqrt(3)*i

5.4   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)]

5.5   a) ((1-i)/(1+i))^4
      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))))

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

5.8   (1-sqrt(3)i)^2-2*(1-sqrt(3)i)+4

5.12  (2+i)*(sqrt(2)/2+sqrt(2)/2*i)*(1/sqrt(2))
      (2+i)*(sqrt(2)/2-sqrt(2)/2*i)*(1/sqrt(2))