## 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

NOTE
• We set the mode to the form that we want our answers in FIRST.
• [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°

NOTE
• We set the mode to the form that we want our answers in FIRST.
• [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]
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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

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
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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]