Question about Texas Instruments TI-84 Plus Calculator

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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.

- define X = a+i*b
- Define Y=c+i*d
- Rewrite the first equation substituting a+i*b for X and c+i*d for y.
- Gather all real terms together, and all imaginary terms together on the left.
- You will have (8a-15b-8c) +i(15a+8b-8d) = 10 +0i
- 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

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

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Posted on Jan 02, 2017

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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.

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

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.

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

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.

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

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.

(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

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.)

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

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

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

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

Press MODE and select one of the two complex modes.

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

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

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

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