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A complex number is a number made up of two components: a real part and an imaginary part It is usually written as a + bi, where a and b are real numbers and i is an imaginary number equal to the square root of 1 Examples of complex numbers are 3+5i, 6 81i and 9 3i PHP s math toolkit doesn t include built-in functions for dealing with complex numbers, so you ll have to turn to PEAR s add-on Math_Complex class, at http:// pearphpnet/package/Math_Complex Here, a complex number object is first generated by passing the number s real and imaginary parts to the object constructor The object s toString() method combines these two components and returns a suitable-for-display string
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You can also do the reverse given a complex number object, you can break it up into its components with the getReal() and getIm() methods, which retrieve the real and imaginary components respectively You can calculate the norm of the number with the norm() method Once you ve got a complex number object, the next step is usually to perform mathematical operations with it The accompanying Math_ComplexOp class provides numerous methods to help you with this The next listing illustrates these methods by generating two complex number objects and performing mathematical operations on them:
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< php // include Math_Complex class include "Math/Complexphp"; // include Math_ComplexOp class include "Math/ComplexOpphp"; // define two complex numbers $complex1 = new Math_Complex(3,2); $complex2 = new Math_Complex(1,4); // add the complex numbers // result: "Sum: 4+6i" $obj = Math_ComplexOp::add($complex1, $complex2); echo "Sum: " $obj->toString() "\n"; // subtract the complex numbers // result: "Difference: 2-2i" $obj = Math_ComplexOp::sub($complex1, $complex2); echo "Difference: " $obj->toString() "\n"; // multiply the complex numbers // result: "Product: -5+14i" $obj = Math_ComplexOp::mult($complex1, $complex2); echo "Product: " $obj->toString() "\n"; // divide the complex numbers // result: "Quotient: 0647058823529 - 0588235294118i" $obj = Math_ComplexOp::div($complex1, $complex2); echo "Quotient: " $obj->toString() "\n";
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2: Working with Numbers
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// invert a complex number // result: "Inverted value: 0230769230769 - 0153846153846i" $obj = Math_ComplexOp::inverse($complex1); echo "Inverted value: " $obj->toString() "\n"; // conjugate a complex number // result: "Conjugated value: 3-2i" $obj = Math_ComplexOp::conjugate($complex1); echo "Conjugated value: " $obj->toString() "\n"; // multiply a complex number and its conjugate // product is always a real number (imaginary part = 0) // result: "Multiplied value: 17 + 0i" $obj = Math_ComplexOp::mult($complex2, Math_ComplexOp:: conjugate($complex2)); echo "Multiplied value: " $obj->toString(); >
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The add(), sub(), mult(), and div() methods take care of complex number addition, subtraction, multiplication, and division respectively The inverse() method returns the inverse of the number, while the conjugate() method returns its conjugate The return value of all these methods is a new Math_Complex object; the actual value of this object can be retrieved using the toString() method
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CHAPTER
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Working with Dates and Times
IN THIS CHAPTER:
31 Getting the Current Date and Time 32 Formatting Timestamps 33 Checking Date Validity 34 Converting Strings to Timestamps 35 Checking for Leap Years 36 Finding the Number of Days in a Month 37 Finding the Day-in-Year or Week-in-Year Number for a Date 38 Finding the Number of Days or Weeks in a Year 39 Finding the Day Name for a Date 310 Finding the Year Quarter for a Date 311 Converting Local Time to GMT 312 Converting Between Different Time Zones 313 Converting Minutes to Hours 314 Converting Between PHP and MySQL Date Formats 315 Comparing Dates 316 Performing Date Arithmetic 317 Displaying a Monthly Calendar 318 Working with Extreme Date Values
PHP Programming Solutions
ike most programming languages, PHP comes with a fairly full-featured set of functions for date and time manipulation Two of these functions are probably familiar to you from your daily work as a developer the date() function for formatting dates and times and the mktime() function for generating timestamps But it s unlikely that you ve had as much contact with the other members of the collection the strtotime() function, the gmdate() function, or the microtime() function These functions, together with many more, make it easy to solve some fairly vexing date/time manipulation problems Over the course of this chapter, I ll show you how to solve such problems, with listings for converting between time zones; checking the validity of a date; calculating the number of days in a month or year; displaying a monthly calendar; performing date arithmetic; and working with date values outside PHP s limits
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