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In C# Please
The Complex class
We are going to model a type that will behave like a complex
number in higher mathematics. We will try to reduce the complexity
of this type by not implementing all of the normal behaviors. There
are 11 members as shown in the class diagram below.
Complex
Class
Properties
+ «property setter absent» Real
:
int
+ «property setter absent»
Imaginary
:
int
+ «computed property» Argument
:
double
+ «computed property» Modulus
:
double
$+ «factory property» Zero
:
Complex
Methods
+ «constructor» Complex(
real = 0
:
int,
imaginary = 0
:
int)
+ ToString()
:
string
$+ «operator» + (lhs : Complex, rhs :
Complex) : Complex
$+ «operator» - (lhs : Complex, rhs :
Complex) : Complex
$+ «operator» == (lhs : Complex, rhs :
Complex) : bool
$+ «operator» != (lhs : Complex, rhs :
Complex) : bool
Description of class members
Properties:
Auto-implemented property is what we have been using so far. You
may not attach code in either the getter or the setter parts.
The first two properties (Real and
Imaginary) are auto-implemented and the rest
(Modulus, Argument and Zero) are
not. These properties are calculated on the fly i.e. whenever they
are required they are calculated.
Real – this int represents the real part of
this type. This is an auto-implemented property, the getter is
public and the setter is absent.
Imaginary – this int represents the imaginary
part of this type. This is an auto-implemented property, the getter
is public and the setter is absent.
Both Modulus and Argument are computed property and Zero is a
factory property.
Modulus – this double represents the complex
modulus or length of this object. It is calculated as the square
root of the sum of the square of the Real and Imaginary parts of
this type
[Real2+Imaginary2 ]. The
getter is public and the setter is absent.
Argument – this double represents the complex
argument or the angle it make with the horizontal axis. It is
calculated as the inverse tan of the ratio of the Real to the
Imaginary part of this type
[tan-1(ImaginaryReal) ]. The getter is public and
the setter is absent.
Zero – this static property returns a new
complex object with both the real and the imaginary parts equal to
0. The getter is public and of course there is no setter.
Constructor:
Complex(int real, int imaginary) – This is
constructor assigns the arguments to the appropriate field
Methods
ToString() – This is a public method overrides
the corresponding method in the object class to return a stringify
form of the object. For this you return the Real and the Imaginary
properties as an ordered pair.
Operators:
public static Complex operator +(Complex lhs, Complex rhs)
The return type
The operator that you want to overload
First operand
Second operand
Signals that you are overloading an operator
+ – You will overload the plus operator to add the two numbers.
Copy the code below into your type declaration to overload the +
operator.
public static Complex
operator +(Complex lhs, Complex rhs)
{
int real = lhs.Real + rhs.Real;
int imaginary = lhs.Imaginary + rhs.Imaginary;
return new Complex(real, imaginary);
}
Some operators have to be overloaded in pairs. This is one of
them.
So you will also have to overload the == and
the != operator at the same time
- – You will also overload the minus
operator. Examine the code above and then try to implement this
operator.
== – You will also overload the
equal-equal operator. Examine the code above and then try to
implement this operator. What should the return type of the method
be?
Test Harness
Insert the following code statements in your Program.cs
file:
Complex c0 = new Complex(-2, 3);
Complex c1 = new Complex(-2, 3);
Complex c2 = new Complex(1, -2);
Console.WriteLine($"{c0}");
Console.WriteLine(c1);
Console.WriteLine(c2);
Console.WriteLine($"{c1} + {c2} = {c1 + c2}");
Console.WriteLine($"{c1} - {c2} = {c1 - c2}");
Complex c3 = c1 + c2;
Console.WriteLine($"{c3} in polar form is
{c3.Modulus:f2}cis({c3.Argument:f2})");
Console.WriteLine($"{c0} {(c0 == c1 ? "=" : "!=")} {c1}");
Console.WriteLine($"{c0} {(c0 == c2 ? "=" : "!=")} {c2}");