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📁 Programming and Problem Solving with C++
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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN" "http://www.w3.org/TR/html4/strict.dtd">	<html>		<head>			<title>page_903</title>			<link rel="stylesheet" href="reset.css" type="text/css" media="all">			<meta http-equiv="Content-Type" content="text/html; charset=UTF-8" />		</head>		<body>		<table summary="top nav" border="0" width="100%">			<tr>				<td align="left" width="30%" style="background: #EEF3E2"><a style="color: blue; font-size: 120%; font-weight: bold; text-decoration: none; font-family: verdana;" href="page_902.html">&lt;&nbsp;previous page</a></td>				<td align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_903</strong></td>				<td align="right" width="30%" style="background: #EEF3E2"><a style="color: blue; font-size: 120%; font-weight: bold; text-decoration: none; font-family: verdana;" href="page_904.html">next page&nbsp;&gt;</a></td>			</tr>					<tr>				<td align="left" colspan="3" style="background: #ffffff; padding: 20px;">    <table border="0" width="100%" cellpadding="0"><tr><td align="center">  <table border="0" cellpadding="2" cellspacing="0" width="100%"><tr><td align="left"></td>  <td align="right"></td>  </tr></table></td></tr><tr><td align="left"><p></p><table border="0" cellspacing="0" cellpadding="0" width="100%"><tr><td align="right"><font face="Times New Roman, Times, Serif" size="2" color="#FF0000">Page 903</font></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"><img src="3e26ecb1b6ac508ae10a0e39d2fb98b2.gif" border="0" width="29" height="1" alt="3e26ecb1b6ac508ae10a0e39d2fb98b2.gif" /></td>  <td colspan="3" height="12"></td>  <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td>  <td><font face="Times New Roman, Times, Serif" size="3">  a Boolean operation that compares two </font><font face="Courier New, Courier, Mono New, Courier, Mono" size="3">Rational</font><font face="Times New Roman, Times, Serif" size="3"> objects for equality</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"><img src="3e26ecb1b6ac508ae10a0e39d2fb98b2.gif" border="0" width="29" height="1" alt="3e26ecb1b6ac508ae10a0e39d2fb98b2.gif" /></td>  <td colspan="3" height="12"></td>  <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td>  <td><font face="Times New Roman, Times, Serif" size="3">  an output operation that displays the value of a </font><font face="Courier New, Courier, Mono New, Courier, Mono" size="3">Rational</font><font face="Times New Roman, Times, Serif" size="3"> object in the form numerator/denominator</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"><img src="3e26ecb1b6ac508ae10a0e39d2fb98b2.gif" border="0" width="29" height="1" alt="3e26ecb1b6ac508ae10a0e39d2fb98b2.gif" /></td>  <td colspan="3" height="12"></td>  <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td>  <td><font face="Times New Roman, Times, Serif" size="3"> Include any additional operations that you think would be useful for a rational number class.</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td>  <td colspan="3" height="12"></td>  <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td>  <td><font face="Times New Roman, Times, Serif" size="3">2. A complex (imaginary) number has the form <i>a + bi,</i> where <i>i</i> is the square root of -1. Here, <i>a</i> is called the real part and <i>b</i> is called the imaginary part. Alternatively, <i>a + bi</i> can be expressed as the ordered pair of real numbers (<i>a, b).</i></font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"><img src="3e26ecb1b6ac508ae10a0e39d2fb98b2.gif" border="0" width="29" height="1" alt="3e26ecb1b6ac508ae10a0e39d2fb98b2.gif" /></td>  <td colspan="3" height="12"></td>  <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td>  <td><font face="Times New Roman, Times, Serif" size="3">Arithmetic operations on two complex numbers (<i>a, b)</i> and (<i>c, d)</i> are as follows:</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td>  <td colspan="3" height="12"></td>  <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td>  <td><font face="Times New Roman, Times, Serif" size="3"><img src="d3711d7fdcfad9a87d646ac6f4f7b5d6.gif" border="0" alt="0903-01.gif" width="223" height="83" /></font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"><img src="3e26ecb1b6ac508ae10a0e39d2fb98b2.gif" border="0" width="29" height="1" alt="3e26ecb1b6ac508ae10a0e39d2fb98b2.gif" /></td>  <td colspan="3" height="12"></td>  <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td>  <td><font face="Times New Roman, Times, Serif" size="3">Also, the absolute value (or magnitude) of a complex number is defined as</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td>  <td colspan="3" height="12"></td>  <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td>  <td><font face="Times New Roman, Times, Serif" size="3"><img src="49bd1a3b890a8d3b128eff2dc40e2d8c.gif" border="0" alt="0903-02.gif" width="107" height="25" /></font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"><img src="3e26ecb1b6ac508ae10a0e39d2fb98b2.gif" border="0" width="29" height="1" alt="3e26ecb1b6ac508ae10a0e39d2fb98b2.gif" /></td>  <td colspan="3" height="12"></td>  <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td>  <td><font face="Times New Roman, Times, Serif" size="3">Design, implement, and test a complex number class that represents the real and imaginary parts as double precision values (data type </font><font face="Courier New, Courier, Mono New, Courier, Mono" size="3">double</font><font face="Times New Roman, Times, Serif" size="3">) and provides at least the following operations:</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"><img src="3e26ecb1b6ac508ae10a0e39d2fb98b2.gif" border="0" width="29" height="1" alt="3e26ecb1b6ac508ae10a0e39d2fb98b2.gif" /></td>  <td colspan="3" height="12"></td>  <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td>  <td><font face="Times New Roman, Times, Serif" size="3"> constructors for explicit as well as default initialization. The default initial value should be (0.0, 0.0).</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"><img src="3e26ecb1b6ac508ae10a0e39d2fb98b2.gif" border="0" width="29" height="1" alt="3e26ecb1b6ac508ae10a0e39d2fb98b2.gif" /></td>  <td colspan="3" height="12"></td>  <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td>  <td><font face="Times New Roman, Times, Serif" size="3"> arithmetic operations that add, subtract, multiply, and divide two complex numbers. These should be implemented as value-returning functions, each returning a class object.</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"><img src="3e26ecb1b6ac508ae10a0e39d2fb98b2.gif" border="0" width="29" height="1" alt="3e26ecb1b6ac508ae10a0e39d2fb98b2.gif" /></td>  <td colspan="3" height="12"></td>  <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td>  <td><font face="Times New Roman, Times, Serif" size="3"> a complex absolute value operation</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"><img src="3e26ecb1b6ac508ae10a0e39d2fb98b2.gif" border="0" width="29" height="1" alt="3e26ecb1b6ac508ae10a0e39d2fb98b2.gif" /></td>  <td colspan="3" height="12"></td>  <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td>  <td><font face="Times New Roman, Times, Serif" size="3"> two observer operations, </font><font face="Courier New, Courier, Mono New, Courier, Mono" size="3">RealPart</font><font face="Times New Roman, Times, Serif" size="3"> and </font><font face="Courier New, Courier, Mono New, Courier, Mono" size="3">ImagPart</font><font face="Times New Roman, Times, Serif" size="3">, that return the real and imaginary parts of a complex number</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"></td>  <td colspan="3" height="12"></td>  <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td>  <td><font face="Times New Roman, Times, Serif" size="3">3. Design, implement, and test a countdown timer class named </font><font face="Courier New, Courier, Mono New, Courier, Mono" size="3">Timer</font><font face="Times New Roman, Times, Serif" size="3">. This class mimics a real-world timer by counting off seconds, starting from an initial value. When the timer reaches zero, it beeps (by sending the alert character, \a, to the standard output device). Some appropriate operations might be the following:</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"><img src="3e26ecb1b6ac508ae10a0e39d2fb98b2.gif" border="0" width="29" height="1" alt="3e26ecb1b6ac508ae10a0e39d2fb98b2.gif" /></td>  <td colspan="3" height="12"></td>  <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td>  <td><font face="Times New Roman, Times, Serif" size="3"> Create a timer, initializing it to a specified number of seconds.</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"><img src="3e26ecb1b6ac508ae10a0e39d2fb98b2.gif" border="0" width="29" height="1" alt="3e26ecb1b6ac508ae10a0e39d2fb98b2.gif" /></td>  <td colspan="3" height="12"></td>  <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td>  <td><font face="Times New Roman, Times, Serif" size="3"> Start the timer.</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"><img src="3e26ecb1b6ac508ae10a0e39d2fb98b2.gif" border="0" width="29" height="1" alt="3e26ecb1b6ac508ae10a0e39d2fb98b2.gif" /></td>  <td colspan="3" height="12"></td>  <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td>  <td><font face="Times New Roman, Times, Serif" size="3"> Reset the timer to some value.</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"><img src="3e26ecb1b6ac508ae10a0e39d2fb98b2.gif" border="0" width="29" height="1" alt="3e26ecb1b6ac508ae10a0e39d2fb98b2.gif" /></td>  <td colspan="3" height="12"></td>  <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td>  <td><font face="Times New Roman, Times, Serif" size="3">When the </font><font face="Courier New, Courier, Mono New, Courier, Mono" size="3">Start</font><font face="Times New Roman, Times, Serif" size="3"> operation is invoked, it should repeatedly decrement and output the current value of the timer approximately every second. To delay the program for one second, use a For loop whose body does absolutely nothing; that is, its body is the null statement. Experiment with the number of loop iterations to achieve as close to a one-second delay as you can.</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table><table border="0" cellspacing="0" cellpadding="0"><tr><td rowspan="5"><img src="3e26ecb1b6ac508ae10a0e39d2fb98b2.gif" border="0" width="29" height="1" alt="3e26ecb1b6ac508ae10a0e39d2fb98b2.gif" /></td>  <td colspan="3" height="12"></td>  <td rowspan="5"></td></tr><tr><td colspan="3"></td></tr><tr><td></td>  <td><font face="Times New Roman, Times, Serif" size="3">If your C++ standard library provides functions to clear the screen and to position the cursor anywhere on the screen, you might want to do the following. Begin by clearing the screen. Then, always display the timer value at the same position in the center of the screen. Each output should overwrite the previous value displayed, just like a real-world timer.</font></td><td></td></tr><tr><td colspan="3"></td></tr><tr><td colspan="3" height="1"></td></tr></table></td></tr></table><p><font size="0"></font></p>  </td>			</tr>				<tr>				<td align="left" width="30%" style="background: #EEF3E2"><a style="color: blue; font-size: 120%; font-weight: bold; text-decoration: none; font-family: verdana;" href="page_902.html">&lt;&nbsp;previous page</a></td>				<td align="center" width="40%" style="background: #EEF3E2"><strong style="color: #2F4F4F; font-size: 120%;">page_903</strong></td>				<td align="right" width="30%" style="background: #EEF3E2"><a style="color: blue; font-size: 120%; font-weight: bold; text-decoration: none; font-family: verdana;" href="page_904.html">next page&nbsp;&gt;</a></td>			</tr>		</table>		</body>	</html>

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