HP 35s User Manual

							 
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HP 33S  Working with Fractions 
 
hp calculators - 5 - HP 33S  Working with Fractions - Version 1.0 
 
 179/3000 is displayed. 
 
 Now store 99 in -. This means that all fractions must be displayed with only one or two digits in the 
denominator. 
 
 99.- 
 
 Figure 9 
 
 The fraction is displayed with only two digits in the denominator, and it is rounded to the nearest possible 
fraction to 179/3000. 
 
 Now display the number with 99 as the denominator. To do this, set flag 8. First, select the flag menu: 
 
 .: 
 
 Figure 10 
 
 This brings up the flags menu. Press  to select the SF (Set Flag) command. Then press ( to select 
flag 8. 
 
 ( 
 
 Figure 11 
  
 The result is now shown as 6/99 but this has been simplified to 2/33. 
 
 To display the fraction with the denominator exactly equal to 99, and no simplification, set flag 9 as well. 
 
 .:9 
 
 Figure 12 
 
 The result is now shown as 6/99 with no simplification. 
 
 Note: with flags 8 and 9 set to force all numbers to be displayed as multiples of 1/c, even zero is now 
displayed that way, so in Figure 12 the number 0 is shown as the fraction 0 0/99. 
   
						

							 
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HP 33S  Working with Fractions 
 
hp calculators - 6 - HP 33S  Working with Fractions - Version 1.0 
 With flags 8 and 9 set, fractions will always be displayed as multiples of the denominator in -. This can 
be very useful in some cases. For example, if a design is being drawn with a ruler marked in 1/16 of an 
inch, it is helpful to put 16 in -, then set flags 8 and 9, and see the results of all calculations as multiples 
of one-sixteenth. 
 
 Finally, to return to the normal display, store 0 in -, and clear flags 8 and 9. Clear flag 7 as well, to see 
that clearing flag 7 does the same as pressing , to cancel fraction display mode. 
 
 2.-.:&8.:&(.:&9 
 
 Figure 13 
 
Answer:  When all the fraction settings are reset to normal, and flag 7 is cleared to cancel fraction display, the 
fraction 179/3000 is displayed as the decimal number 0.060 to three decimal places. 
 
Note: for more information about flags, see the training aid on flags. 
   
						

							 
 
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HP 35s  Working with complex numbers –part 1 
 
 
 
 
Complex numbers 
 
Practice working problems involving complex numbers 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
   
						

							 
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HP 35s  Working with complex numbers – part 1 
 
hp calculators - 2 - HP 35s  Working with complex numbers – part 1 - Version 1.0 
Complex numbers 
 
Complex numbers occur in problems facing several disciplines, from quantum mechanics to working with magnetic 
fields. They are also useful in modeling the flow of a fluid around a pipe. They even show up in the solution of a 
differential equation that models the up and down movement of a car’s shock absorber. They are also used to describe 
the inductance and capacitance of electrical circuits, for example, using the formula E = I x Z, where E is voltage, I is 
current, and Z is impedance. In many electricity and electronics areas, the “i” of an imaginary number is usually 
represented as “j” to avoid any confusion with the variable “I” which represents current in electronics formulas. 
 
To distinguish complex numbers from real numbers, the HP 35s has a dedicated 6 key, which is pressed between the 
real and imaginary part of a complex number. Because the HP 35s holds an entire complex number in one stack 
register, the entire 4-level stack can hold 4 complex numbers at once. 
 
In RPN mode, the HP 35s has two “complex number” modes available. The first is the standard xiy mode, where the real 
portion is input, the key pressed, and then the complex number portion is input. The second is by entering the complex 
number in “polar” format or a magnitude r, then the theta symbol, followed by an angle, or simply r!a. These are 
selected using the !8 menu choices 9 and 10 as shown in figure 1. To choose option 9 once !8 has 
been pressed, press 9. To choose option 10, press the decimal point followed by a zero. 
 
 Figure 1 
 
In algebraic mode, the HP 35s has three “complex number” modes available. The first two modes are the same as for 
RPN and are described in the preceding paragraph. The third mode which is only available in algebraic is the x+yi mode. 
It is selected using the !8 menu choice 11, as shown in figure 2. To choose option 11 if you have already 
pressed !8, press the decimal point followed by a one. 
 
 Figure 2 
 
Note that changing the display mode changes any previously entered complex numbers to the new format. This means 
that to convert from polar to rectangular coordinates, for example, all that is needed is to change how a polar form 
complex number is displayed. 
 
The HP 35s provides a new level of ease of use when dealing with complex numbers. 
 
Practice working problems involving complex numbers 
 
Example 1: Compute (2+3i) * [(7-6i) + (4+5i)]. Use the XiY display mode. 
 
Solution: Press !8! 
 
 In RPN mode, perform the addition of the two complex numbers and then the multiplication: 
 
 6#$%&6()6*+   
						

							 
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HP 35s  Working with complex numbers – part 1 
 
hp calculators - 3 - HP 35s  Working with complex numbers – part 1 - Version 1.0 
 In algebraic mode: 
 
 )6*+46#$(&6% 
 
 Figure 3 
 
 Figure 4 
 
Answer: 25 + 31i. Figure 3 shows the display in RPN mode. Figure 4 shows the display in algebraic mode. 
 
Example 2: In Radians mode, compute sin(2+3i) + cos(1-4i) + e(2+2i) 
 
Solution: In RPN mode: 
 
 9)  (Sets Radians mode) 
 )6*,6&$#()6)-$( 
 
 In algebraic mode: 
 
 9) (Sets Radians mode) 
 )6*%(#,6&$%-$)6)% 
 
 Figure 5 
 
Answer: The approximate answer is 20.83 + 25.51i. Figure 5 shows the display in algebraic mode. 
 
Example 3: Find 3+2i divided by 4-4i. 
 
Solution: In RPN mode: 
 
 *6)%&6&$. 
 
 In algebraic mode: 
 
 *6).&6&$% 
 
 Figure 6   
						

							 
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HP 35s  Working with complex numbers – part 1 
 
hp calculators - 4 - HP 35s  Working with complex numbers – part 1 - Version 1.0 
Answer: The answer is 0.125 + 0.625i. Figure 6 shows the answer in RPN mode 
 
Example 4: For the complex number 5+6i, find the magnitude of the vector represented. 
 
Solution: In RPN or algebraic mode:  
 *6)%!8& 
 
 Figure 7 
 
 Figure 8 
 
Answer: The answer of 7.8102 is shown in the display. Figure 7 shows the answer in RPN mode. Note that if the 
magnitude is needed separated from the number shown, the () function will provide it (this is 
shown in Figure 8). If the angle is desired separated from the number shown, the *= function will 
provide it.  
Example 5: The voltage in a circuit is 45 + 5j volts and the impedance is 3 + 4j ohms. Find the total current.  
Solution: Using the equation E = I x Z, the current I is equal to E / Z.  
 In RPN mode:  
 &6%*6&.  
 In algebraic mode:  
 &6.*6&% 
 
 Figure 9  
Answer: The answer is 6.2 – 6.6i. This is equivalent to 6.2 - 6.6j amps. Figure 9 shows the answer in RPN mode.    
						

							 
 
hp calculators 
 
 
 
 
HP 35s  Working with complex numbers – Part 2 
 
 
 
 
Complex numbers 
 
Practice working problems involving complex numbers 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
   
						

							 
hp calculators 
 
HP 35s  Working with complex numbers – part 2 
 
hp calculators - 2 - HP 35s  Working with complex numbers – part 2 - Version 1.0 
Complex numbers 
 
Complex numbers occur in problems facing several disciplines, from quantum mechanics to working with magnetic 
fields. They are also useful in modeling the flow of a fluid around a pipe. They even show up in the solution of a 
differential equation that models the up and down movement of a car’s shock absorber. They are also used to describe 
the inductance and capacitance of electrical circuits, for example, using the formula E = I x Z, where E is voltage, I is 
current, and Z is impedance. In many electricity and electronics areas, the “i” of an imaginary number is usually 
represented as “j” to avoid any confusion with the variable “I” which represents current in electronics formulas. 
 
To distinguish complex numbers from real numbers, the HP 35s has a dedicated 6 key, which is pressed between the 
real and imaginary part of a complex number. Because the HP 35s holds an entire complex number in one stack 
register, the entire 4-level stack can hold 4 complex numbers at once. 
 
In RPN mode, the HP 35s has two “complex number” modes available. The first is the standard xiy mode, where the real 
portion is input, the key pressed, and then the complex number portion is input. The second is by entering the complex 
number in “polar” format or a magnitude r, then the theta symbol, followed by an angle, or simply r!a. These are 
selected using the !8 menu choices 9 and 10 as shown in figure 1. To choose option 9 once !8 has 
been pressed, press 9. To choose option 10, press the decimal point followed by a zero. 
 
 Figure 1 
 
In algebraic mode, the HP 35s has three “complex number” modes available. The first two modes are the same as for 
RPN and are described in the preceding paragraph. The third mode which is only available in algebraic is the x+yi mode. 
It is selected using the !8 menu choice 11, as shown in figure 2. To choose option 11 if you have already 
pressed !8, press the decimal point followed by a one. 
 
 Figure 2 
 
Note that changing the display mode changes any previously entered complex numbers to the new format. This means 
that to convert from polar to rectangular coordinates, for example, all that is needed is to change how a polar form 
complex number is displayed. 
 
The HP 35s provides a new level of ease of use when dealing with complex numbers. 
 
Practice working problems involving complex numbers 
 
Example 1: Compute (2+3i) * [(7-6i) + (4+5i)]. Use the x+yi display mode in algebraic mode 
 
Solution: Put the HP 35s into algebraic by pressing 9!. Then press !8 
 
 4#$%6#&44$()6#$4*$+6,   
						

							 
hp calculators 
 
HP 35s  Working with complex numbers – part 2 
 
hp calculators - 3 - HP 35s  Working with complex numbers – part 2 - Version 1.0 
 Figure 3 
 
Answer: 25 + 31i. Figure 3 shows the display in algebraic mode. 
 
Example 2: Extract the X and Y coordinates of the complex number 5!30. Use degrees mode. 
 
Solution: Changing the display mode to !8$ will convert the complex number to an X and Y form. 
However, to extract the X and Y values, it is necessary to leave the display in polar form using the 
%& function to extract the magnitude and the = function to extract the angle. Once 
extracted, the X and Y coordinates can be computed for further use as follows: 
 
 X = r COS ! 
 Y = r SIN ! 
 
 In either RPN or algebraic mode: 
 
 9  (Sets degrees mode) 
 !8( 
 )-?%(, 
 
 In algebraic mode: 
 
 %&%*#&+=%*, 
 
 Figure 4 
 
 )-?%(,%&%*#&,=%*, 
 
 Figure 5 
 
 In RPN mode: 
 
 %&%*=+& 
 
 Figure 6   
						

							 
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HP 35s  Working with complex numbers – part 2 
 
hp calculators - 4 - HP 35s  Working with complex numbers – part 2 - Version 1.0 
 -%&%*=,& 
 
 Figure 7 
 
Answer: The X coordinate is approximately 4.33 and the Y coordinate is 2.5.  Figures 4 and 5 show the display in 
algebraic mode. Figures 6 and 7 show the display in RPN mode. 
 
Example 3: Use the HP 35s to verify the triangle inequality for two complex numbers, which states that if z and w are 
any two complex numbers, then |z + w|  |z| + |w|. 
 
 Use the complex numbers z = 3 + 1i and w = -1+2i 
 
Solution: 9  (Sets degrees mode) 
 !8( 
  
 In RPN mode, compute |z + w| first. 
 
 %6.,.)6#$ 
 
 Figure 8 
 
 The magnitude of the resulting complex number will be approximately 3.6. It is computed by pressing: 
 %& 
 
 Figure 9 
 
In RPN mode, now compute |z| + |w|. 
 
%6.%& 
 .)6#%& 
 $ 
 
 Figure 10 
 
Answer: The results verify the triangle inequality. The individual magnitudes of the two complex numbers added 
together is larger than the magnitude of the result from adding the complex numbers together.