01 July 2010

Complex Arithmetic on the TI-89 Titanium® (phasor practice)

This blog will show you how to add, subtract, multiply, and divide complex numbers in both polar and rectangular form.

Before we proceed with the calculator, let's make sure we know what's going on.  If you need to brush up, here is a fantastic link.  Also, note that the complex conjugates are:

A* = 2.5 - (-)j3.8 = 2.5 + j3.8 and C* = 4.1<-48°.

Let's say we have four equations of complex numbers.  Two are in rectangular form and two are in polar form.

A = 2.5 - j3.8   B = -1.7 + j2.3   C = 4.1 <48° D = 2.5 <-6°

Now, to start, you must also know that a) you cannot multiply or divide complex coordinates in rectangular form and b) you cannot add or subtract complex coordinates in polar form directly--that's what your calculator is for you big dummy!
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For this section we will give our answers in rectangular form.

Express C in rectangular form: C = 2.74 + j3.05

On your calculator:
NOTE
  • We set the mode to the form that we want our answers in FIRST.  
  1. Set up your environment:
  • [MODE] >> [scroll down to 'Complex Format'] >> [right arrow ('>')] >> [scroll to 'RECTANGULAR' and press enter OR press 2] >> [enter]
  • [MODE] >> [scroll down to 'Angle'] >> [right arrow ('>')] >> [scroll  to 'DEGREE' and press enter OR press 2] >> [enter]
  1. If not at your home screen, press [HOME]
  2. Enter: 
NOTE
  • (make the '<' by pressing [2ND] >> [EE])
  • (4.1<48) [enter] 
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 For this section we will give our answers in polar form.

Express A in polar form: A = 4.5 <-56.7°

On your calculator:
NOTE
  • We set the mode to the form that we want our answers in FIRST.  
  1. Set up your environment:
  • [MODE] >> [scroll down to 'Complex Format'] >> [right arrow ('>')] >> [scroll to 'POLAR' and press enter OR press 3] >> [enter]
  • [MODE] >> [scroll down to 'Angle'] >> [right arrow ('>')] >> [scroll  to 'DEGREE' and press enter OR press 2] >> [enter]
  1. If not at your home screen, press [HOME]
  2. Enter: 
NOTE
  • (make the i by pressing [2ND] >> [CATALOG])
  • 2.5 - i3.8 [enter]
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Now, if you can convert polar form to rectangular form and vice versa, you are in good shape!

Obviously, I can't go through each permutation for you (that would be 32 different combinations).  So, I will show an addition problem and a multiplication problem.
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For this section we will add two expressions in polar form and express the answer in rectangular form.

C + D = 4.1<48° + 2.5<-6°

On your calculator (assuming you followed along up above, I will just bust out the steps in a direct format, omit steps as you see fit):

  1. [MODE] >> [scroll down to 'Complex Format'] >> [right arrow ('>')] >> [scroll to 'RECTANGULAR' and press enter OR press 2] >> [enter]
  2. [MODE] >> [scroll down to 'Angle'] >> [right arrow ('>')] >> [scroll  to 'DEGREE' and press enter OR press 2] >> [enter]
  3.  (4.1<48) + ( 2.5<-6) [enter]
  4. answer: 5.2 + j2.8
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For this section we will multiply two expressions in rectangular form and express the answer in polar form.

A * B = 2.5 - j3.8 * -1.7 + j2.3

On your calculator:
  1. [MODE] >> [scroll down to 'Complex Format'] >> [right arrow ('>')] >> [scroll to 'POLAR' and press enter OR press 3] >> [enter]
  2. [MODE] >> [scroll down to 'Angle'] >> [right arrow ('>')] >> [scroll  to 'DEGREE' and press enter OR press 2] >> [enter]
  3. 2.5 - i3.8 * -1.7 + i2.3
  4. answer: 9.1<74.1°
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Notes:
  • polar coordinates must have parenthesis around them (i.e. '(3.4<45)' )
  • You can also use the menus to convert rectangular coordinates to polar coordinates and vice versa:
  •  (3.4<45) [2ND] [5] [scroll to 'MATRIX' and press right arrow or press 4] [scroll to Vector ops and press right arrow] [scroll to 'arrow' Rect] [enter]
  • answer: 3.4 + j.3
  • setting up your environment in the beginning because you know what form you want your answer in helps out a lot
  • You can also convert those nasty trigonometric values into real numbers by simply multiplying your answer by 1.0 (e.g. ans*1.0)
  • Here is a link to the dummies books for more info. 
  • Also, note the order of operations for your calc.  If you have to multiply a bunch of stuff and divide it by something, don't waste time with the parenthesis.  The TI-89 will multiply first and then divide. 
  • Another neat trick.  Say you are looking to get the magnitude of a vector in polar coordinates to use in your next calculation (e.g. the vector 25<-43.0).  You can grab the absolute value of the vector (if ans = 25<-43.0) by hitting:
    • [2nd] [5]
    • [right arrow]
    • [abs(]
    • [2nd] [(-)] (this should give you abs(ans()) = 25)
 Enjoy!

12 comments:

Anonymous said...

This is a very informative site.

Eric said...

2.5 - i3.8 * -1.7 + i2.3
answer: 9.1<74.1°

The first time, I put my complex numbers in ( ) and got a different answer. The second time I typed it exactly as you have it and I got what your answer. Why can I not use ( )?

staticd said...

"2.5 - i3.8 * -1.7 + i2.3
answer: 9.1<74.1°

The first time, I put my complex numbers in ( ) and got a different answer. The second time I typed it exactly as you have it and I got what your answer. Why can I not use ( )?"

First, I am not sure why you would want to use more keys than you have to...

The calculator operates under the same rules we do.

In order to multiply rectangular, the calculator converts to polar and then does the multiplication.

If you put the parentheses, the calculator FOILs the rectangular and then converts the result to polar.

Anonymous said...

when i put in 4.1<48 and hit enter i get a syntax error.

any idea?

Anonymous said...

must use () around it

Anonymous said...

(4.1<48)

Unknown said...

Thank you so much!

Anonymous said...

Thanks,
That was helpful!

Anonymous said...

i am new with the calculator and when i put minus angle in polar form, a get a syntax.Any ideas ?

Patrick Chung said...

Now there is online tool for complex phasors of AC signals adding and drawing in both complex and time domain fashion. Please visit:
http://www.cirvirlab.com/simulation/complex_number_phasor_addition_online.php#.UW-NycqzmhE

Jaykers said...

(2.5-3.8i)*(-1.7+2.3i) = 9.1<74.1 is wrong. if you do this calculation out by hand the polar forms are 4.54863<-56.65 and 2.86<126.469 respectively. ... 4.55*2.86 ~= 13 . Use your parenthesis.

staticd said...

Jaykers is correct. I made a mistake there. Thanks for pointing that out.