test_polar = ->
  run_test [
    "polar(1+i)",
    "2^(1/2)*exp(1/4*i*pi)",

    "polar(-1+i)",
    "2^(1/2)*exp(3/4*i*pi)",

    "polar(-1-i)",
    "2^(1/2)*exp(-3/4*i*pi)",

    "polar(1-i)",
    "2^(1/2)*exp(-1/4*i*pi)",

    "rect(polar(3+4*i))",
    "3+4*i",

    "rect(polar(-3+4*i))",
    "-3+4*i",

    "rect(polar(3-4*i))",
    "3-4*i",

    "rect(polar(-3-4*i))",
    "-3-4*i",

    "rect(polar((-1)^(1/2)))",
    "i",

    "rect(polar((-1)^(-5/6)))",
    "-1/2*i-1/2*3^(1/2)",

    "rect(polar((-1)^(-5/a)))",
    "cos(5*pi/a)-i*sin(5*pi/a)",

    "rect(polar((-1)^(a)))",
    "cos(a*pi)+i*sin(a*pi)",

    "-i*(-2*rect(polar((-1)^(1/6)))/rect(polar((3^(1/2))))+2*rect(polar((-1)^(5/6)))/rect(polar((3^(1/2)))))^(1/4)*(2*rect(polar((-1)^(1/6)))/rect(polar((3^(1/2))))-2*rect(polar((-1)^(5/6)))/rect(polar((3^(1/2)))))^(1/4)/(2^(1/2))",
    #"-(-1)^(3/4)",
    "1/2^(1/2)-i/(2^(1/2))",

    # this is also "-(-1)^(3/4)" but we get to that after the simplification after
    # this test
    "-i*(-2*polar((-1)^(1/6))/polar((3^(1/2)))+2*polar((-1)^(5/6))/polar((3^(1/2))))^(1/4)*(2*polar((-1)^(1/6))/polar((3^(1/2)))-2*polar((-1)^(5/6))/polar((3^(1/2))))^(1/4)/(2^(1/2))",
    "-i*(-2*exp(1/6*i*pi)/(3^(1/2))+2*exp(5/6*i*pi)/(3^(1/2)))^(1/4)*(2*exp(1/6*i*pi)/(3^(1/2))-2*exp(5/6*i*pi)/(3^(1/2)))^(1/4)/(2^(1/2))",

    "simplify",
    "(1-i)/(2^(1/2))",

    "-i*(-2*rect(exp(1/6*i*pi))/(3^(1/2))+2*rect(exp(5/6*i*pi))/(3^(1/2)))^(1/4)*(2*rect(exp(1/6*i*pi))/(3^(1/2))-2*rect(exp(5/6*i*pi))/(3^(1/2)))^(1/4)/(2^(1/2))",
    #"-(-1)^(3/4)",
    "1/2^(1/2)-i/(2^(1/2))",

    "polar(-(-1)^(3/4))",
    "exp(-1/4*i*pi)",

    "polar(-i*(-2*(-1)^(1/6)/(3^(1/2))+2*(-1)^(5/6)/(3^(1/2)))^(1/4)*(2*(-1)^(1/6)/(3^(1/2))-2*(-1)^(5/6)/(3^(1/2)))^(1/4)/(2^(1/2)))",
    "exp(-1/4*i*pi)",

    # nothing to do for polar since we end
    # up with a real
    "polar((-1)^(1/6) - (-1)^(5/6))",
    "3^(1/2)",

  ]