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!
___________________________________________________
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] 

___________________________________________________
 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]

___________________________________________________
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.
___________________________________________________
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

___________________________________________________
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°

___________________________________________________

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!