ABSTRACT CLASSES AND INTERFACES - Introduction to Java Programming: Comprehensive Version - page 532

You can also obtain the absolute value for a complex number using the following
formula:

a 2 b 2

a + bi = 2 +

(A complex number can be interpreted as a point on a plane by identifying the ( a,b )
values as the coordinates of the point. The absolute value of the complex number
corresponds to the distance of the point to the origin, as shown in Figure 13.10b.)
Design a class named Complex for representing complex numbers and the
methods add , subtract , multiply , divide , and abs for performing complex-
number operations, and override toString method for returning a string repre-
sentation for a complex number. The toString method returns (a + bi) as a
string. If b is 0 , it simply returns a . Your Complex class should also implement the
Cloneable interface.
Provide three constructors Complex(a, b) , Complex(a) , and Complex() .
Complex() creates a Complex object for number 0 and Complex(a) cre-
ates a Complex object with 0 for b . Also provide the getRealPart() and
getImaginaryPart() methods for returning the real and imaginary part of the
complex number, respectively.
Write a test program that prompts the user to enter two complex numbers and
displays the result of their addition, subtraction, multiplication, division, and abso-
lute value. Here is a sample run:

Enter the first complex number: 3.5 5.5
Enter the second complex number: -3.5 1
(3.5 + 5.5i) + (-3.5 + 1.0i) = 0.0 + 6.5i
(3.5 + 5.5i) - (-3.5 + 1.0i) = 7.0 + 4.5i
(3.5 + 5.5i) * (-3.5 + 1.0i) = -17.75 + -13.75i
(3.5 + 5.5i) / (-3.5 + 1.0i) = -0.5094 + -1.7i
|(3.5 + 5.5i)| = 6.519202405202649

13.18

( Use the Rational class ) Write a program that computes the following summa-
tion series using the Rational class:

1
2

2
3

3
4

98
99

99
100

+ + + c + +

You will discover that the output is incorrect because of integer overflow (too
large). To fix this problem, see Programming Exercise 13.15.

13.19

( Convert decimals to fractions ) Write a program that prompts the user to enter
a decimal number and displays the number in a fraction. Hint: read the decimal
number as a string, extract the integer part and fractional part from the string,
and use the BigInteger implementation of the Rational class in Programming
Exercise 13.15 to obtain a rational number for the decimal number. Here are some
sample runs:

Enter a decimal number: 3.25
The fraction number is 13/4