HP Free42 User Manual

Yes it is possible, but who wants to calculate the square root of –1 every time, to have i?
We can use the  COMPLEX function to take register y and register x of the stack and create a
complex number y + ix. Again unlike HP-33S almost all the functions of the HP-42S fully support
complex numbers.
Example: Show that i
2
is √–1.
Solution: 0 ENTER 1  COMPLEX  x
2
which gives -1.0000 i0.0000 (means -1).
5.2 Complex numbers in polar coordinates
When representing a point in R
2
we can use any kind of coordinate system. The most commonly used
are the rectangular (or Cartesian system) which use the usual coordinates x and y and the polar system
which use the coordinates r and θ. The relationship between them is x = r cos θ, y = r sin θ and
r =
(x
2
+ y
2
)
1/2
, θ = tan
–1
y/x. When dealing with complex numbers we can think of the real axis as being
the x axis and the imaginary axis as being the y axis in Cartesian coordinates, or we can use also polar
coordinates. In this case i will be r = 1 and θ = π/2 (90°).To change between rectangular or polar
modes use RECT and POLAR in the  MODES menu.
6 Programming
Programming the HP-42S is very simple and very versatile. It does not use the RPL style of the HP-
48 or HP-49. You program in the same way you use the calculator and unlike some non-HP cheaper
calculators, all the steps are shown in the display and in numbered lines.
6.1 Basic programming
Let's imagine you want to make a given calculation. For example: Suppose you want to solve a
equation x
2
–5x + 4 = 0 which is of the form ax
2
+ bx + c = 0. As you know the solution for this kind
of equation is
a
b
x
2
Δ±−
=
where Δ = b
2
– 4ac. Let's suppose a, b and c are in R
00
, R
01
and R
02
respectively and we are going to
use R
03
for ∆. To solve this equation using HP-42S/Free42 we just do
RCL 01 (This is b)
x
2
4
RCL 00 (This is a)
RCL 02 (This is c, keep in mind we have only four lines in the stack)
×
×
–
STO 03 (This is ∆)
Unlike some other models, say 33S, we don't need to worry whether ∆ is negative. But we save the
square root for later because in R
03
the number cannot be complex. (otherwise we would need to store
it in a normal memory)
Now we calculate the first root
RCL 01

HP Free42 Specifications

General

Brand	HP
Model	Free42
Category	Calculator
Language	English

Summary

1 Introduction

2 Basic Operations

2.1 RPN

Explains Reverse Polish Notation (RPN) and its usage on the HP-42S calculator.

2.2 Turn ON/OFF

2.3 Setting the display contrast

Describes how to adjust the calculator's display contrast.

2.4 Training RPN using HP-42S

Provides exercises to practice RPN calculations on the HP-42S.

2.6 DISP Menu

2.6.1 The FIX function

Explains how to set a fixed number of decimal places for display.

2.6.3 The SCI function

Explains how to set the calculator to scientific notation display.

2.6.4 The ENG function

Details how to set the calculator to engineering notation display.

2.7 MODES Menu

2.8 The Stack

Explains the internal stack registers (X, Y, Z, T) used in RPN calculations.

2.9 Getting used to some keys of the keyboard

1/x and Vx Functions

Explains the reciprocal and square root keys.

LOG and 10^X Functions

Describes the base-10 logarithm and its inverse functions.

XEQ and GTO Functions

Introduces functions for program execution and branching.

3 Memory

STO and Arithmetic STO Functions

Explains how to store values in memory registers and perform arithmetic operations.

Storing Named Variables

Details storing values using alphabetic names instead of register numbers.

3.2 More on the CLEAR menu

CATALOG Menu: FCN Submenu

Lists all available functions, including hyperbolic and programming functions.

CATALOG Menu: REAL Submenu

Lists variables containing real numbers, excluding numbered registers.

3.3 The CUSTOM Menu

4 Probability

Introduces statistical functions for probability calculations.

Probability Function: COMB

Calculates the number of combinations of N things taken r at a time.

5 Complex Numbers

5.1 Complex Numbers in Rectangular Coordinates

Explains how to represent and work with complex numbers in rectangular form.

Probability Function: PERM

Calculates the number of permutations of N things taken r at a time.

6 Programming

5.2 Complex Numbers in Polar Coordinates

Details how to represent and use complex numbers in polar coordinates.

6.1 Basic Programming

Introduces fundamental concepts and steps for writing programs on the HP-42S.

Program Lines and Navigation

Program Execution and Output

Covers how programs run, stop, and display results.

6.2 More Than One Program in Memory

Using the GTO Command

Explains how the GTO command is used to navigate between program spaces and labels.

Creating and Using Labels

Defines labels and how they are used with GTO and XEQ for program branching.

6.3 Conditional Branching: X?0 and X?Y Sub-menus

6.4 Real Program Examples

Program Example: Timer

Demonstrates a simple "timer" program using conditional branching.

Program Example: Prime Number Check

Shows a program to determine if a number is prime.

7 Using the Solver

Solving Quadratic Equations with Solver

Demonstrates using the solver to find roots of quadratic equations.

8 Numeric Integration

Solver Example: Ideal Gas Equation

Shows how to use the solver for the ideal gas law equation PV=nRT.

9 Statistics

Entering Statistical Data

Explains how to input data for one-variable and two-variable statistics.

Statistical Functions Overview

Lists and briefly describes available statistical functions like SUM, MEAN, SDEV.

9.2 Statistical Modes: ALLE, LINE, EREG, ERG?

10 Matrices

MATRIX Menu: NEW Function

Explains how to create a new matrix of a specified size.

MATRIX Menu: INV Function

Describes how to calculate the inverse of a matrix.

MATRIX Menu: DET Function

Details how to calculate the determinant of a matrix.

Matrix Editing Example

Solving Linear Systems with Matrices

Explains how matrices can be used to solve systems of linear equations.

Complex Matrix Creation

DOT and CROSS Product Functions

Explains the calculation of dot and cross products for vectors.

11 Other Bases

BASE Menu Functions

Covers functions for hexadecimal, decimal, octal, and binary modes.

12 Flags

Flag Management Functions

Describes functions to set, clear, and test flags.

Specific Flag Meanings

Explains the purpose of specific flags like audio, display grouping, and auto-off.

13 Free42-Specific Features

13.1 Keyboard Interface

Maps calculator keys to a standard computer keyboard layout for Free42.

13.2 Program Import and Export

Details how to import and export programs to/from Free42.

13.3 Printing

Explains options for printing calculator output to text or graphics files.

14 Comprehensive Command List

Command List: ABS

Absolute value. Returns |x|.

Command List: ACOS

Arc cosine. Returns cos¯¹ x.

Command List: DET

Determinant. Returns the determinant of the matrix.

Command List: GTO

Go to label or branch to a specified label.

Command List: OFF

Turn the calculator off (programmable).

Command List: RND

Round the number in the x-register.

Command List: XEQ

Execute a function or program.