Sharp EL546W Calculator
Vectors and Complex Numbers
Introduction
This material is designed to review the basic Vector arithmetic functions and settings of the
Sharp EL546W Scientific Calculator.
Angle Notation
DRG
The 3 angle formats can be set in the SET UP menu:
Angle format
To set, touch:
Display
Degree
SET UP ; 0 ; 0
DEG
Radian
SET UP ; 0 ; 1
RAD
Gradian
SET UP ; 0 ; 2
GRAD
Angle Notation is set with the DRG function in the SET UP menu.
Vectors are represented as complex numbers
 Rectangular form:......................................................................................................x  yi
 Polar form:...................................................................................................................r
Vector computations are performed in the CPLX mode on the Sharp EL546W calculator.
Settings
 Set angle format to DEG:....................................................... Enter:
SET UP ; 0 ; 0
 Set calculator mode to CPLX:.......................................................... Enter
MODE 3
note the xy or r on the display (upper left corner)
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Function Keys
In CPLX mode, the following additional calculator function keys are relevant:

i


The vector angle symbol ............................................... Enter:

 r
Converting to Polar form............................................... Enter:
2nd F 8

 xy
Converting to Rectangular form................................... Enter:
2nd F 9

, 
Accessing a second component.......................... Enter:
The imaginary unit ............................................................... Enter:
ab/c
D°MS
2nd F
Exp
Vector Results - Display Form
The results of vector calculations can appear in either Polar form r or Rectangular form
x  yi.
 Rectangular form x  yi............................................................... display indicator:
xy
 Polar form.................................................................................... display indicator:
r
Setting Display Form for Vector Results
To set the display form, first set the calculator to CPLX mode.
 Set calculator mode to CPLX:.......................................................... Enter
MODE 3
 To set xy form.................................................................................................. 2nd F  xy
display (upper right corner) indicates:
xy
 To set r form................................................................................................... 2nd F  r
display (upper right corner) indicates:
r
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Entering Vectors
With the calculator in CPLX mode, a vector can be entered in either Polar form r or
Rectangular form x  yi.
 Polar Form:....................................................................................................................r
Example:
5 kN 53. 13 °.................................................. Enter:
5  53. 13 
 Rectangular Form:.............................................................................................. x  y i
Example:
Enter the vector with components:
x  3 kN and y  4 kN............................................................................ 3  4 i 
Rectangular to Polar (xy to r) Conversions
To determine the magnitude r and the direction  for a vector, knowing its x and y
components:
 Enter the Rectangular form...........................................................................................x  y i
 Set the Display form to ............................................................................................................ r
 The Display provides the magnitude ....................................................................................... r
 To Display the Direction  ...................................................................................... 2nd F , 
Example:
Determine the magnitude r and the direction  for a vector, knowing its x component is 12 kN
and its y component is 8 kN:
 Enter the Rectangular form..................................................................................... 12  8 i 
 Set the Display form to r....................................................................................... 2nd F  r
 Display provides the magnitude r.................................................................................... 14. 422
 To Display the Direction: 2nd F ,  .......................................................................... 33. 69
The Polar form is ................................................................................................14. 422 kN 33. 69 °
Answer:
The polar components of the vector 12  8i are:
..................................................................................................................................... r  14. 422 kN
..........................................................................................................................................   33. 69 °
Sharp EL546W - Vectors (SharpEL546WVectors.tex)................................................................. 3
Polar to Rectangular (r to xy) Conversions
To determine the x and y components of a vector, knowing its magnitude r and direction  :
 Enter the Polar form........................................................................................................r  
 Set the Display form to ............................................................................................................xy
 The Display provides the x component ................................................................................... x
 To Display the y component .................................................................................. 2nd F , 
Example:
Determine the x and y components of the vector 24. 5 kN 124 °.
 Enter the Polar form........................................................................................... 24. 5  124 
 Set the Display form to xy...................................................................................... 2nd F  xy
 Display provides the x component...................................................................................13. 70
 To Display the y component: 2nd F ,  ......................................................................20. 31i
The Rectangular form is ..........................................................................................13. 70  20. 31i
Answer:
The vector components of 24. 5 kN 124 ° are:
..................................................................................................................................... x  13. 70 kN
..................................................................................................................................... y  20. 31 kN
Sharp EL546W - Vectors (SharpEL546WVectors.tex)................................................................. 4
Vector Addition
The process of adding vectors provides the resultant for a system of vectors.
 In CPLX mode, vectors are added as complex numbers.
 Vectors can be added in either Rectangular or Polar form or a combination of both
forms.
 The Resultant r  or its x and y components are determined by selecting the
appropriate Display form.
Example:
Determine the resultant of the three forces, 15 kN 70 ° , 10 kN 30 ° and 12 kN 320 °
Enter:................................................................................ 15  70  10  30  12  320 
The display will depend on the form set.
 In xy form:.............................................................................. displays x component:
22. 983
for the y component: enter 2nd F ,  ......................................................................11. 382i
That is, the resultant components are:
.............................................................................. x component:
22. 98 kN
.............................................................................. y component:
11. 38 kN
 In r form: ............................................................................... displays magnitude r:
for the angle  :.................................................. entering 2nd F ,  displays:
That is, .................................................................................the resultant is:
25. 647
26. 346
25. 65 kN 26. 35 °
Online Documents
The online Scientific Notebook version of this document can be accessed from within
Scientific Notebook by pasting the following URL into the dialogue under FileOpen
Location.:
http://www.mohawkcollege.ca/dept/math/EL546W/SharpEL546WVectors.tex
The online Adobe PDF version of this document can be accessed from any web browser,
with the URL:
http://www.mohawkcollege.ca/dept/math/EL546W/SharpEL546WVectors.pdf
Sharp EL546W - Vectors (SharpEL546WVectors.tex)................................................................. 5