public double getModulus()
{
double square = MAL.Power(real, 2) + MAL.Power(imaginary, 2);
double complement = MAL.SquareRoot(square, InstantiationDecimals);
return(complement);
}
public Complex(double m, double a, bool w)//Constructive method for modulus argument.
{
argument = MAL.Round(a, InstantiationDecimals);
modulus = MAL.Round(m, InstantiationDecimals);
real = MAL.Round((m * MAL.Cos(a)), InstantiationDecimals);
imaginary = MAL.Round((m * MAL.Sin(a)), InstantiationDecimals);
}
public Complex(double r, double i)
{
real = MAL.Round(r, InstantiationDecimals);
imaginary = MAL.Round(i, InstantiationDecimals);
modulus = MAL.Round(getModulus(), InstantiationDecimals);
argument = MAL.Round(getArgument(), InstantiationDecimals);
}
private static Complex multiplyAndDivide(Complex x, Complex y, bool division)
{
double pi = MAL.Pi();
double resultantModulus;
double resultantArgument;
if (division)
{
resultantModulus = x.modulus / y.modulus;
resultantArgument = x.argument - y.argument;
}
else//This occurs when division is false
{
resultantModulus = x.modulus * y.modulus;
resultantArgument = x.argument + y.argument;
}
if (resultantArgument > pi)
{
resultantArgument -= 2 * pi;
}
if (resultantArgument < -pi)
{
resultantArgument += 2 * pi;
}
Complex resultantNumber = new Complex(resultantModulus, resultantArgument, true);
return(resultantNumber);
}
public string outputRealImaginary()
{
string realImag;
if (imaginary < 0)
{
realImag = Convert.ToString(MAL.Round(real, OutputDecimals)) + Convert.ToString(MAL.Round(imaginary, OutputDecimals)) + "i";
}
else
{
realImag = Convert.ToString(MAL.Round(real, OutputDecimals)) + " + " + Convert.ToString(MAL.Round(imaginary, OutputDecimals)) + "i";
}
return(realImag);
}
private void Graph_Load(object sender, EventArgs e)
{
Width = ScreenWidth / CentreOfGraphScale - ScreenHeight / 4;
Height = Width;
Location = new Point(startingX, startingY);
double[] scalingTest = new double[2];
double scalingTrial;
switch (typeOfGraph)
{
case "MIDPOINT":
scalingTest[0] = Values.Max();
scalingTest[1] = MAL.Modulus(Values.Min());
scalingTrial = scalingTest.Max();
significantFigures = MAL.Exponent(scalingTrial, ScaleBase);
ScalingFactor = MAL.Power(ScaleBase, significantFigures);
break;
case "HALFLINE":
scalingTest[0] = MAL.Modulus(Values[0]);
scalingTest[1] = MAL.Modulus(Values[1]);
scalingTrial = scalingTest.Max();
significantFigures = MAL.Exponent(scalingTrial, ScaleBase);
ScalingFactor = MAL.Power(ScaleBase, significantFigures);
break;
case "CIRCLE":
scalingTest[0] = MAL.Modulus(Values[0]);
scalingTest[1] = MAL.Modulus(Values[1]);
scalingTrial = scalingTest.Max() + Values[2];
significantFigures = MAL.Exponent(scalingTrial, ScaleBase);
ScalingFactor = MAL.Power(ScaleBase, significantFigures);
break;
case "DISPLAY":
scalingTest[0] = MAL.Modulus(Values[0]);
scalingTest[1] = MAL.Modulus(Values[1]);
scalingTrial = scalingTest.Max();
significantFigures = MAL.Exponent(scalingTrial, ScaleBase);
ScalingFactor = MAL.Power(ScaleBase, significantFigures);
break;
}
}
public double getArgument()
{
double Pi = MAL.Pi();
if (real == 0)
{
if (imaginary < 0)
{
return(-Pi / 2);
}
else if (imaginary > 0)
{
return(Pi / 2);
}
else
{
return(0);
}
}
double x = MAL.Modulus(imaginary / real);
double angle = MAL.Arctan(x);
if (real < 0 && imaginary < 0)
{
angle = angle - Pi;
}
else if (real < 0)
{
angle = Pi - angle;//This is the part that has changed - the geometry is now correct.
}
else if (imaginary < 0)
{
angle = -angle;
}
return(angle);
}
public string outputModulusArgument()
{
string modulusArgument = Convert.ToString(MAL.Round(modulus, OutputDecimals)) + "(cos" + Convert.ToString(MAL.Round(argument, OutputDecimals)) + " + isin" + Convert.ToString(MAL.Round(argument, OutputDecimals)) + ")";
return(modulusArgument);
}
private void Graph_Paint(object sender, PaintEventArgs e)
{
double Unit = Width / 22;
Pen blackPen = new Pen(Brushes.Black, 2);
Pen redPen = new Pen(Brushes.Red, 3);
Font font = new Font("Microsoft Sans Serif", (int)(5 * Unit / 9 - (MAL.Modulus(significantFigures - 1))));
SolidBrush brush = new SolidBrush(Color.Black);
e.Graphics.DrawLine(blackPen, Width / CentreOfGraphScale, 0, Width / CentreOfGraphScale, Height);
e.Graphics.DrawLine(blackPen, 0, Height / CentreOfGraphScale, Width, Height / CentreOfGraphScale);
for (int i = 1; i <= 21; i++)
{
if (i != 11)
{
e.Graphics.DrawLine(blackPen, (float)(i * Unit + Unit / 10), Height / CentreOfGraphScale - Height / 80, (float)(i * Unit + Unit / 10), Height / CentreOfGraphScale + Height / 80);
e.Graphics.DrawLine(blackPen, Width / CentreOfGraphScale - Width / 80, (float)(i * Unit + Unit / 10), Width / CentreOfGraphScale + Width / 80, (float)(i * Unit + Unit / 10));
}
}
int n = 1;
for (int i = -10; i <= 10; i++)
{
PointF ImagAxis;
PointF RealAxis;
if (i % 2 == 0)
{
ImagAxis = new PointF(Width / CentreOfGraphScale + Width / 55, (float)(Height - (n * Unit) - Unit / CentreOfGraphScale));
RealAxis = new PointF((float)(n * Unit - Unit / 3), Width / CentreOfGraphScale + Width / 125);
}
else
{
RealAxis = new PointF((float)outOfRangeValue, (float)outOfRangeValue);
ImagAxis = new PointF((float)outOfRangeValue, (float)outOfRangeValue);
}
if (i == 0)
{
ImagAxis = new PointF((float)outOfRangeValue, (float)outOfRangeValue);
}
string number = Convert.ToString(i * ScalingFactor);
e.Graphics.DrawString(number, font, brush, RealAxis);
e.Graphics.DrawString(number, font, brush, ImagAxis);
n++;
}
switch (typeOfGraph)
{
case "MIDPOINT":
Complex Coordinates1 = new Complex(Values[0], Values[2]);
Complex Coordinates2 = new Complex(Values[1], Values[3]);
Complex Midpoint = Complex.calculateMidpoint(Coordinates1, Coordinates2);
double Gradient = Complex.calculatePerpendicularGradient(Coordinates1, Coordinates2);
//Scale the graph to accept large and small values; also makes the coordinates relative to the centre of the graph.
//Scaling and drawing coordinates centrally is used later.
//Below is how the bisector is drawn.
e.Graphics.DrawLine(redPen, Width / 2 + (float)(Unit * (Midpoint.real / ScalingFactor - 22)), Width / CentreOfGraphScale - (float)(Unit * (Midpoint.imaginary / ScalingFactor - Gradient * 22)), Width / CentreOfGraphScale + (float)(Unit * (Midpoint.real / ScalingFactor + 22)), Width / CentreOfGraphScale - (float)(Unit * (Midpoint.imaginary / ScalingFactor + Gradient * 22)));
//Draws coordinates of complex numbers as crosses.
e.Graphics.DrawLine(redPen, Width / CentreOfGraphScale + (float)(Unit * (Coordinates1.real / ScalingFactor - DrawCrossCoordinates)), Width / CentreOfGraphScale - (float)(Unit * (Coordinates1.imaginary / ScalingFactor - DrawCrossCoordinates)), Width / CentreOfGraphScale + (float)(Unit * (Coordinates1.real / ScalingFactor + DrawCrossCoordinates)), Width / CentreOfGraphScale - (float)(Unit * (Coordinates1.imaginary / ScalingFactor + DrawCrossCoordinates)));
e.Graphics.DrawLine(redPen, Width / CentreOfGraphScale + (float)(Unit * (Coordinates1.real / ScalingFactor - DrawCrossCoordinates)), Width / CentreOfGraphScale - (float)(Unit * (Coordinates1.imaginary / ScalingFactor + DrawCrossCoordinates)), Width / CentreOfGraphScale + (float)(Unit * (Coordinates1.real / ScalingFactor + DrawCrossCoordinates)), Width / CentreOfGraphScale - (float)(Unit * (Coordinates1.imaginary / ScalingFactor - DrawCrossCoordinates)));
e.Graphics.DrawLine(redPen, Width / CentreOfGraphScale + (float)(Unit * (Coordinates2.real / ScalingFactor - DrawCrossCoordinates)), Width / CentreOfGraphScale - (float)(Unit * (Coordinates2.imaginary / ScalingFactor - DrawCrossCoordinates)), Width / CentreOfGraphScale + (float)(Unit * (Coordinates2.real / ScalingFactor + DrawCrossCoordinates)), Width / CentreOfGraphScale - (float)(Unit * (Coordinates2.imaginary / ScalingFactor + DrawCrossCoordinates)));
e.Graphics.DrawLine(redPen, Width / CentreOfGraphScale + (float)(Unit * (Coordinates2.real / ScalingFactor - DrawCrossCoordinates)), Width / CentreOfGraphScale - (float)(Unit * (Coordinates2.imaginary / ScalingFactor + DrawCrossCoordinates)), Width / CentreOfGraphScale + (float)(Unit * (Coordinates2.real / ScalingFactor + DrawCrossCoordinates)), Width / CentreOfGraphScale - (float)(Unit * (Coordinates2.imaginary / ScalingFactor - DrawCrossCoordinates)));
break;
case "HALFLINE":
Complex endCoordinates = new Complex(32, Values[2], true); //Creates a new complex number with the same argument and a modulus outside the graph.
//Draws the halfline.
e.Graphics.DrawLine(redPen, Width / CentreOfGraphScale + (float)(Unit * Values[0] / ScalingFactor), Width / CentreOfGraphScale - (float)(Unit * Values[1] / ScalingFactor), Width / CentreOfGraphScale + (float)(Unit * (endCoordinates.real + Values[0] / ScalingFactor)), Width / CentreOfGraphScale - (float)(Unit * (endCoordinates.imaginary + Values[1] / ScalingFactor)));
//Draws starting coordinates of complex number as a cross.
e.Graphics.DrawLine(redPen, Width / CentreOfGraphScale + (float)(Unit * (Values[0] / ScalingFactor - DrawCrossCoordinates)), Width / CentreOfGraphScale - (float)(Unit * (Values[1] / ScalingFactor - DrawCrossCoordinates)), Width / CentreOfGraphScale + (float)(Unit * (Values[0] / ScalingFactor + DrawCrossCoordinates)), Width / CentreOfGraphScale - (float)(Unit * (Values[1] / ScalingFactor + DrawCrossCoordinates)));
e.Graphics.DrawLine(redPen, Width / CentreOfGraphScale + (float)(Unit * (Values[0] / ScalingFactor - DrawCrossCoordinates)), Width / CentreOfGraphScale - (float)(Unit * (Values[1] / ScalingFactor + DrawCrossCoordinates)), Width / CentreOfGraphScale + (float)(Unit * (Values[0] / ScalingFactor + DrawCrossCoordinates)), Width / CentreOfGraphScale - (float)(Unit * (Values[1] / ScalingFactor - DrawCrossCoordinates)));
break;
case "CIRCLE":
try
{
//The radius must be subtracted from a for x and added to b for y as DrawPie uses (x,y) as coordinates of top left corner of the square surrounding the circle.
e.Graphics.DrawPie(redPen, Width / CentreOfGraphScale + (float)(Unit * (Values[0] - Values[2]) / ScalingFactor), Width / CentreOfGraphScale - (float)(Unit * (Values[1] + Values[2]) / ScalingFactor), (float)(Unit * Values[2] * 2 / ScalingFactor), (float)(Unit * 2 * Values[2] / ScalingFactor), 360, 360); //diameter = 2*radius.
//Draws centre as a cross
e.Graphics.DrawLine(redPen, Width / CentreOfGraphScale + (float)(Unit * (Values[0] / ScalingFactor - DrawCrossCoordinates)), Width / CentreOfGraphScale - (float)(Unit * (Values[1] / ScalingFactor - DrawCrossCoordinates)), Width / CentreOfGraphScale + (float)(Unit * (Values[0] / ScalingFactor + DrawCrossCoordinates)), Width / CentreOfGraphScale - (float)(Unit * (Values[1] / ScalingFactor + DrawCrossCoordinates)));
e.Graphics.DrawLine(redPen, Width / CentreOfGraphScale + (float)(Unit * (Values[0] / ScalingFactor - DrawCrossCoordinates)), Width / CentreOfGraphScale - (float)(Unit * (Values[1] / ScalingFactor + DrawCrossCoordinates)), Width / CentreOfGraphScale + (float)(Unit * (Values[0] / ScalingFactor + DrawCrossCoordinates)), Width / CentreOfGraphScale - (float)(Unit * (Values[1] / ScalingFactor - DrawCrossCoordinates)));
}
catch
{
MessageBox.Show("Error: The circle must have a positive radius");
}
break;
case "DISPLAY":
e.Graphics.DrawLine(redPen, Width / CentreOfGraphScale, Width / CentreOfGraphScale, Width / CentreOfGraphScale + (float)(Unit * (Values[0] / ScalingFactor)), Width / CentreOfGraphScale - (float)(Unit * (Values[1] / ScalingFactor)));
e.Graphics.DrawLine(redPen, Width / CentreOfGraphScale + (float)(Unit * (Values[0] / ScalingFactor - DrawCrossCoordinates)), Width / CentreOfGraphScale - (float)(Unit * (Values[1] / ScalingFactor - DrawCrossCoordinates)), Width / CentreOfGraphScale + (float)(Unit * (Values[0] / ScalingFactor + DrawCrossCoordinates)), Width / CentreOfGraphScale - (float)(Unit * (Values[1] / ScalingFactor + DrawCrossCoordinates)));
e.Graphics.DrawLine(redPen, Width / CentreOfGraphScale + (float)(Unit * (Values[0] / ScalingFactor - DrawCrossCoordinates)), Width / CentreOfGraphScale - (float)(Unit * (Values[1] / ScalingFactor + DrawCrossCoordinates)), Width / CentreOfGraphScale + (float)(Unit * (Values[0] / ScalingFactor + DrawCrossCoordinates)), Width / CentreOfGraphScale - (float)(Unit * (Values[1] / ScalingFactor - DrawCrossCoordinates)));
break;
}
}
