Method tan

src/org/opensourcephysics/numerics/Complex.java:560–596

Returns the tangent of this complex number.

()

   * Returns the tangent of this complex number.
   */
  public Complex tan() {
    // tan(z) = sin(z)/cos(z)
    double izRe, izIm;
    double temp1Re, temp1Im;
    double temp2Re, temp2Im;
    double scalar;
    Complex sinResult, cosResult;
    //  sin(z)  =  ( exp(i*z) - exp(-i*z) ) / (2*i)
    izRe = -im;
    izIm = re;
    // first exp
    scalar = Math.exp(izRe);
    temp1Re = scalar*Math.cos(izIm);
    temp1Im = scalar*Math.sin(izIm);
    // second exp
    scalar = Math.exp(-izRe);
    temp2Re = scalar*Math.cos(-izIm);
    temp2Im = scalar*Math.sin(-izIm);
    temp1Re -= temp2Re;
    temp1Im -= temp2Im;
    sinResult = new Complex(0.5*temp1Re, 0.5*temp1Im);
    //  cos(z)  =  ( exp(i*z) + exp(-i*z) ) / 2
    izRe = -im;
    izIm = re;
    // first exp
    scalar = Math.exp(izRe);
    temp1Re = scalar*Math.cos(izIm);
    temp1Im = scalar*Math.sin(izIm);
    // second exp
    scalar = Math.exp(-izRe);
    temp2Re = scalar*Math.cos(-izIm);
    temp2Im = scalar*Math.sin(-izIm);
    temp1Re += temp2Re;
    temp1Im += temp2Im;
    cosResult = new Complex(0.5*temp1Re, 0.5*temp1Im);
    return sinResult.div(cosResult);
  }

  //------------------------------------------------------------------------
  // Inverse trigonometric functions