1. COMPUTER 2430 Object Oriented Programming and Data Structures I

2. Complex Numbers Real numbers Imaginary numbers 5i i = i * i = -1
a + bi, where both a and b are real numbers … -2 -1 1 2

3. Complex Numbers b a
a + bi

4. Operations on Complex Numbers
(a1 + b1i) + (a2 + b2i) = (a1 + a2) + (b1 + b2)i
(a1 + b1i) - (a2 + b2i) = (a1 - a2) + (b1 - b2)i
(a1 + b1i) * (a2 + b2i) = (a1 * a2 - b1 * b2) +
(a1 * b2 + a2 * b1)i
(a1 + b1i) / (a2 + b2i) =
((a1 + b1i) * (a2 - b2i)) / ((a2 + b2i) * (a2 - b2i))
(a2 + b2i) * (a2 - b2i) = (a2 * a2 + b2 * b2)
Conjugate of a + bi is a – bi
Magnitude of a + bi is

5. Complex Numbers b a
a + bi

6. ADT: Complex Number Data Two double (float): real and imag
String representation
(real, imag)
Could be a + bi
Or other formats

7. Complex Class public class Complex { private double real, imag;
public Complex() // Default constructor
real = imag = 0.0; }
public Complex( Complex z ) // Copy constructor
real = z.real; // this.real = z.real;
imag = z.imag; // this.imag = z.imag;
...

8. More Constructors public class Complex { private double real, imag;
...
public Complex( double realPart, double imagPart )
real = realPart;
imag = imagPart; }
public Complex( double realPart )
imag = 0.0;

9. public class Complex {
private double real, imag;
public Complex( double realPart, double imagPart )
real = realPart;
imag = imagPart; }
/**
Does not change either instance, this or parameter z.
Usage: z3 = z1.plus(z2); */
public Complex plus ( Complex z )
return new Complex( real + z.real, imag + z.imag );

10. public class Complex {
private double real, imag;
public Complex( double realPart, double imagPart )
. . . }
/**
Does not change either instance, this or parameter z. */
public Complex plus ( Complex z )
return new Complex( this.real + z.real,
this.imag + z.imag );

11. Override Method toString
public class Complex {
private double real, imag;
...
/**
Example: (3.4, 12.8) */
@Override
public String toString()
return "(" + real + ", " + imag + ")"; }

12. Override Method equals
public class Complex {
private double real, imag;
@Override
public boolean equals ( ? ) }

13. Override Method equals
public class Complex {
private double real, imag;
@Override
public boolean equals ( Object obj )
if ( obj instanceof Complex )
Complex temp = (Complex) obj;
return (real == temp.real && imag == temp.imag); }
return false;

14. public class Complex {
private double real, imag;
. . .
public Complex divides ( Complex z )
public Complex conjugate()
public double magnitude()
public boolean lessThan( Complex z )
public boolean hasSameMagnitude( Complex z ) }

15. Test 1
Wednesday, October 10
Note01 - Note14
50 points

16. Program 2 Due 10 pm, October 5 Follow instructions
-1 by 10 pm, October 6
-5 by 10 pm, October 8
Follow instructions
Individual Assignment
Do it yourself!

17. Program 3 Due Wednesday, October 24 Lab 4 Lab 5 Part of Prog3
Due 10 pm, Monday, October 15
Lab 5
Due 10 pm, Wednesday, October 17