Question about Texas Instruments TI-84 Plus Calculator

1 Answer

I am trying to solve imaginary number equations with matrix using the TI-84 For example: (8+15i)x-8y = 10 -8x-(8-10i)y = 0 8+15i -8 10 -8 8-10i 0 should i convert to another form?

Posted by on

Ad

1 Answer

  • Level 3:

    An expert who has achieved level 3 by getting 1000 points

    Superstar:

    An expert that got 20 achievements.

    All-Star:

    An expert that got 10 achievements.

    MVP:

    An expert that got 5 achievements.

  • Texas Instru... Master
  • 8,081 Answers

I am afraid you cannot use the TI8xPlus family of calculators to solve linear systems in matrix form. In this calculator, matrices must have real coefficients.
You can however separate (expand) the problem into a linear system of 4 equations in 4 unknowns and try to solve it with the calculator.

  1. define X = a+i*b
  2. Define Y=c+i*d
  3. Rewrite the first equation substituting a+i*b for X and c+i*d for y.
  4. Gather all real terms together, and all imaginary terms together on the left.
  5. You will have (8a-15b-8c) +i(15a+8b-8d) = 10 +0i
  6. This equation can be split into two equations by saying that
  • the real part pf the left member is equal to the real part of the right member, this gives 8a-15b-8c=10, and
  • the imaginary part of the left member is equal to the imaginary part of the right member, this gives 15a+8b-8d=0
Similarly, you rewrite the second complex equation substituting a+ib for X and c+id for Y, then expand the binomial products, gather the real parts on the left together, and the imaginary parts on the left together. After that you equate the real part on the left to the real part on the right, and do the same for the imaginary parts.

If I did not make mistakes during the expansions and the gathering of terms you should get the following equation
-(8a+8c+10d) +i*(-8b+10c-8d) =0+i*0 from which you extract an equation for the real parts, -(8a+8c+10d)=0 and another for the imaginagy parts i*(-8b+10c-8d) =i*0

If I did not make mistakes (you should be able to find them, if any) your system of two linear equations with complex coefficents has been converted to a system of 4 linear equations with real coefficients.

8a-15b-8c=10
15a+8b-8d=0
8a+8c+10d=0
-8b+10c-8d =0

Now, you can in theory solve this system with help of the calculator, to find a, b, c, and d. When these are found, you can reconstruct the X and Y solutions.

Now get to work: Ascertain that my extracted equations are correct, then solve for a, b,c, and d, and reconstruct X and Y.
I am no seer, but my hunch is that this system is degenarate. I will not explain what that means.

Posted on Feb 11, 2010

  • k24674 Feb 11, 2010

    Sorry, I am indeed no seer and apparently the matrix is non singular. Again, if I did not make mistakes its determinat is -78884, so it can be inverted. Good Luck.

×

Ad

1 Suggested Answer

6ya6ya
  • 2 Answers

SOURCE:

Hi there,
Save hours of searching online or wasting money on unnecessary repairs by talking to a 6YA Expert who can help you resolve this issue over the phone in a minute or two.

Best thing about this new service is that you are never placed on hold and get to talk to real repairmen in the US.

Here's a link to this great service

Good luck!

Posted on Jan 02, 2017

Ad

Add Your Answer

Uploading: 0%

my-video-file.mp4

Complete. Click "Add" to insert your video. Add

×

Loading...
Loading...

Related Questions:

1 Answer

Edit Casio FX - 9860G SD have complex equations??


Thhe Casio FX-9860G SD can solve a polynomial equation of degree 2 or 3 with REAL coefficients. If the complex MODE is set to REAL it will find the real roots. If the complex mode is set to a+ib, it will find the real and complex roots.

Apparently it will take coefficients that are real, and will give a Ma Error if any coefficient is complex.

Addendum.
The calculator CANNOT solve equations with complex coefficient. YOU can however convert the system of linear equations with ccomplex coefficients ( of the type you show) as a system of 4 linear equations in 4 unknowns; Split x into a real and an imaginary part, split y into a real and an imaginary part. Substitute Real(x)+iIm(x) for variable x in the equations; substitute Real(y)+iIm(y) for y in the two equations; do the algebra. In each of the original equations split the Real and imaginary parts. You should be able to derive 4 linear equations in unknowns Real(x), Im(x), Real(y), and Im(y).
Use the linear equation solver to obtain the solutions. Recompose x=Real(x)+iIm(x), and y=Real(y)+iIm(y)

Alternatively, after you create the system of 4 linear equations you can use the matrix utility to find Real(x), Im(x), Real(y) and Im(y) and recompose the x and y.

Mar 17, 2012 | Casio FX-9860G Graphic Calculator

1 Answer

My TI 84 won't convert my imaginary numbers to fractions. I typed in 1/(1+i) and it won't convert the answer to fraction form. It keeps saying Error Data Type


The TI-84 works with real fractions. It will not convert complex numbers to fractions.

You can convert the real and imaginary components to fractions separately. For your example, 1/(1+i) is .5-.5i. Converting .5 and -.5 to fractions, you get 1/2 + (1/2)i.

Sep 15, 2011 | Texas Instruments TI-84 Plus Calculator

1 Answer

Hello How to solve complex equations using casio fx 9860G AU For example (2+i)A+B=6 2A+(1+i)B=1 How to solve A and B using this calculator


The simultaneous equation solver requires the coefficients to be real. Similarly matrices must have real coefficients.
Your only alternative is to express each of A and B as a real part and imaginary part.
A= x1+iy1
B=x2+iy2.
Substitute x1+iy1 for A in the two equations. Substitute x2+iy2 for B in the two equations. Do the algebra. Gather real parts and gather imaginary parts. Split each original equation into two equations: One equation comes from setting Real Part of left side = real part of right side (1); the other equations comes from setting the imaginary part of left side= imaginary part of right side (here 0).

Do the same procedure for the 2nd original equation.
At the end of the process you will have 4 coupled linear equations in the 4 unknowns (x1,y1,x2,y2).

Then you might want to use the calculator to solve the derived system. Once you have x1,y1,x2,y2 you reconstruct A=x1+iy1, etc.

Aug 29, 2011 | Casio FX-9860G Graphic Calculator

1 Answer

2c + 6 + 7c = 8


To solve this with a ti-84 press [math] and select solve from the menu. This will open the equation solver. Type in your equation
(Note: you may need to put it in the form with 0=, So the equation would be 0 = 2c + 6 +7c - 8 ). Then press
enter or arrow down button.

Mar 30, 2011 | Texas Instruments TI-84 Plus Calculator

1 Answer

5/4x-18=-3 Ti 84 plus One: just press enter/solve Two: press 2nd Test (Math) then press enter Every time I put in and equation using the above method for the equal sign. it either takes me back to...


If you wan to solve an equation using the SOLVE feature you enter it as follows (your example)
You should rewrite it as 5/4*X-18+3 (= 0). Implicitly, the calculator assumes that the right side is ZERO and you do not enter any right side nor an equal sign.
Type in
5/4 [*] [X,T,theta, n] -18 +3 [ALPHA] [ENTER] (SOLVE)
You should get an answer -780/47 or the decimal equivalent (depending on display mode.)

Feb 12, 2011 | Texas Instruments TI-84 Plus Calculator

1 Answer

HOW TO INPUT IMAGINARY NUMBERS INTO A MATRIX


Unfortunately, you can't. From the most recent guidebook: "You can store only real numbers in TI-84 matrices. Fractions are stored as real numbers and can be used in matrices."

Sep 07, 2010 | Texas Instruments TI-84 Plus Calculator

2 Answers

Steps in solving matrix on my ti 89 calculator.


I assume you are speaking of solving a system of equations with a number of unknowns. If not, please correct me. Here's an example in practice:

If you have a system of 3 equations with 3 unknowns, you would set up your matrix so that the coefficients of each variable for a particular equation are on one row. So, given equations x + y + z = 0, 2x + 3y - 4z = 1, x + -z = -1 you would type the following into your calculator: [[1,1,1,0][2,3,-4,1][1,0,-1,-1]] and press enter to make sure you typed it correctly. notice that in the third row there is a zero, since we have zero time y for the third equation. Then row-reduce the matrix (2nd > 5 > 4 > 4 or in the CATALOG as rref). You should get out the matrix [[1,0,0,-1][0,1,0,1][0,0,1,0]]. This says that x=-1 y = 1 z=0 since my first column contained the coefficients for the x variable, the second for the y variable, and the third for the z variable. The last column contains the solution, the part on the other side of the equals sign.

Hope this helps! For more reading (from someone else; I just made this one up), check out the Wikipedia articles on Gaussian elimination and Systems of linear equations

May 03, 2009 | Texas Instruments TI-84 Plus Calculator

2 Answers

Using imaginary numbers in a matrix


Press MODE and select one of the two complex modes.

Mar 30, 2009 | Texas Instruments TI-84 Plus Calculator

2 Answers

How do you use the imaginary number with the TI-84 calculator?


If you want the answer in rectangular form, set MODE a+bi and tap ENTER and QUIT. Tap square root sign, tap (-)4 and close the parenthesis and tap ENTER. The answer is shown as 2i.
If you want the answer in polar form, set MODE to re^xi and and DEGREE. Tap ENTER and QUIT. Tap the square root sign, tap (-)4, close the parenthesis, and tap ENTER. The answer shown is 2e^90i. (2 at ninety degrees). If you selected RADIAN mode, the answer would be 2e^1.57i (2 at 1.57 radians; or 2 at pi/2 radians)

Mar 09, 2009 | Texas Instruments TI-86 Calculator

3 Answers

IF I HAVE TWO equations 5x+8y=54, AND -9x+y=26 how do i solve


use the simultaneous equation solver software available on ur ti-89 and enter the equation in the form of augmented matrix and you will get ur answer.

Dec 03, 2008 | Texas Instruments TI-89 Calculator

Not finding what you are looking for?
Texas Instruments TI-84 Plus Calculator Logo

1,357 people viewed this question

Ask a Question

Usually answered in minutes!

Top Texas Instruments Office Equipment & Supplies Experts

k24674

Level 3 Expert

8081 Answers

Steve Allison
Steve Allison

Level 3 Expert

5569 Answers

Ekse

Level 3 Expert

13434 Answers

Are you a Texas Instruments Office Equipment and Supply Expert? Answer questions, earn points and help others

Answer questions

Manuals & User Guides

Loading...