# NAG Library Chapter Introduction

## 1Scope of the Chapter

This chapter provides facilities for arithmetic operations involving complex numbers.

## 2Background to the Problems

Of the several representations used for complex numbers, perhaps the most common is $a+ib$, where $a$ and $b$ are real numbers, and $i$ represents the imaginary number $\sqrt{-1}$. The number $a$ is the real part, and $ib$ the imaginary part.
For the basic arithmetic operations of addition, subtraction and multiplication, the inclusion of routines was not considered worthwhile. Their coding would be short and no special techniques need be used.
In complex number operations of a more complicated nature, special precautions may have to be taken to avoid unnecessary overflow and underflow at intermediate stages of the computation. This has led to the inclusion of routines in this chapter.

## 3Recommendations on Choice and Use of Available Routines

The routines were originally written for use by NAG Library routines which compute eigensystems of real and complex matrices (see Chapter F02). They may, however, be of general use to programmers using complex numbers.
Fortran programmers may prefer to use the COMPLEX facilities in that language rather than carrying the real and imaginary parts of the numbers in different variables.

## 4Functionality Index

 Complex numbers,
 division a02acf
 modulus a02abf
 square root a02aaf

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