HP 15c Collector's Edition User Manual

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Section 11
Calculating With
Complex Numbers
The HP 15c enables you to calculate with complex numbers, that is,
numbers of the form
a + ib,
where a is the real part of the complex number,
b is the imaginary part of the complex number, and
i = √ −1.
As you will see, the beauty of calculating with the HP 15c in Complex mode
is that once the complex numbers are keyed in, most operations are
executed in the same manner as with real numbers.
The Complex Stack and Complex Mode
Calculations with complex numbers are
performed using a complex stack
composed of two parallel four-register
stacks (and two LAST X registers). One of
these parallel stacks—referred to as the
real stack—contains the real parts of
complex numbers used in calculations.
(This is the same stack used in ordinary
calculations.) The other stack—referred
to as the imaginary stack—contains the
imaginary parts of complex numbers
used in calculations.
Creating the Complex Stack
The imaginary stack is created (by converting five storage registers as
described in Appendix C) when you activate Complex mode; it does not
exist when the calculator is not in Complex mode.
Real
Stack
Imaginary
Stack
T
Z
Y
X
LAST X

HP 15c Collector's Edition Specifications

General

Model	HP 15c Collector's Edition
Category	Calculator
Type	Scientific
Power Source	Battery
Manufacturer	HP
Display	LCD
Functions	complex numbers, matrix operations

Summary

Introduction

This Handbook

Outlines the structure of the manual, detailing its parts and how to use it for learning.

The HP Community

Discusses user groups and websites for HP calculator enthusiasts and information sharing.

Part I: HP 15c Fundamentals

Section 1: Getting Started

Covers basic operations like powering on, keyboard layout, and primary/alternate functions.

Section 2: Numeric Functions

Explains essential numeric operations including logs, trig, powers, and conversions.

Section 3: The Automatic Memory Stack, LAST X, and Data Storage

Details the RPN stack, LAST X register, and data storage operations.

Part II: HP 15c Programming

Section 6: Programming Basics

Introduces core programming concepts: creating, loading, running programs, and memory.

Section 8: Program Branching and Controls

Covers controlling program flow using branching, loops, and conditional tests.

Part III: HP 15c Advanced Functions

Section 11: Calculating With Complex Numbers

Covers entering, manipulating, and performing calculations with complex numbers.

Section 12: Calculating With Matrices

Explains matrix operations, including dimensioning, element access, and calculations.

Section 13: Finding the Roots of an Equation

Details using the SOLVE function for numerical root finding and equation solving.

Section 14: Numerical Integration

Explains how to perform numerical integration using the ∫f(x)dx key and subroutines.

Appendix A: Error Conditions

Error 8: No Root

Explains the error when the SOLVE function cannot find a root.

Error 0: Improper Mathematics Operation

Lists and explains errors related to mathematical operations and illegal arguments.

Appendix D: A Detailed Look at SOLVE

How SOLVE Works

Explains the numerical technique and logic behind the SOLVE algorithm.

Finding Several Roots

Discusses methods for finding multiple roots of an equation using the SOLVE function.