# Complex Numbers In Polar Coordinates; Programming; Basic Programming - HP -42S Manual

An alternative: hp-42s calculator and free42 simulator for palmos.

Yes it is possible, but who wants to calculate the square root of –1 every time, to have i?
We can use the
COMPLEX
complex number y + ix. Again unlike HP-33S almost all the functions of the HP-42S fully support
complex numbers.
Example: Show that i
Solution: 0 ENTER 1

## 5.2 Complex numbers in polar coordinates

When representing a point in R
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 =
2
2
1/2
–1
(x
+ y
)
, θ = tan
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

### 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
2
equation x
–5x + 4 = 0 which is of the form ax
of equation is
2
where Δ = b
– 4ac. Let's suppose a, b and c are in R
use R
for ∆. To solve this equation using HP-42S/Free42 we just do
03
RCL 01 (This is b)
2
x
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
it in a normal memory)
Now we calculate the first root
RCL 01
function to take register y and register x of the stack and create a
2
is √–1.
2
COMPLEX
x
which gives -1.0000 i0.0000 (means -1).
2
we can use any kind of coordinate system. The most commonly used
MODES
±
b
=
x
2
a
the number cannot be complex. (otherwise we would need to store
03
2
+ bx + c = 0. As you know the solution for this kind
Δ
, R
and R
00
01
02
respectively and we are going to