Complex numbers on a calculator

[Axioms]

Hey I just want to find out if anyone knows if it is possible to enter complex numbers into a matrix of a scientific calculator.

 

I have a CASIO fx-991ES PLUS scientific calculator.

 

For example:

 

If 20cos(200t -45)= 70jI1 + 90jI2 .....1

 

and 0=2jI1 +8jI2 ....... 2

 

Is there any way to solve these equations in a 2x2 matrix on a calculator? (The j's are imaginary, used so that there is no confusion with the variable vectors of I1 and I2).

 

It is easy to solve these equations by hand but when it gets up to 4 equations to solve it gets far more tricky and time consuming. I am getting fed up with all the math that is involved to solve simple circuits, so I thought I'd come here and see if anyone has any advise.

 

I have tried every possible method in trying to put the complex numbers into the calculator but it just keeps changing it back to real numbers and ignoring the imaginary numbers.

 

Any help would be appreciated.

[Pixel]

CASIO FX-991ES PLUS Manual - Page E-18 shows you how to input complex numbers.

 

I am unsure about inputting them into a matrix however. Good luck.

[Axioms]

I know how to input complex numbers. I am just unsure if it is possible to input complex numbers in a matrix for the calculator to solve. I have lost my manual so thanks.

 

I don't think it is possible because it cannot even solve for a variable if there are complex numbers in the equation. I guess I'm just hoping that there is a function on the calculator that I have not heard of before that can solve many equations of complex numbers simutaneously.

[DJBruce]

No idea about whether or not your calculator can handle complex matrices. However, since there is a natural homeomorphism from [latex]\mathbb{C}^{n}[/latex] to [latex]\mathbb{R}^{2n}[/latex], and so also a nice homeomorphism from [latex]M_{n\times n}\left(\mathbb{C}\right)[/latex] to [latex]M_{2n\times 2n}\left(\mathbb{R}\right)[/latex], you can just use real matrices to try and solve your system.

Edited May 29, 2012 by DJBruce

[Xittenn]

I'm sorry DJBruce but is homeomorphism the proper word or should you not be using homomorphism? I'm not so sure a matrix itself can be considered a topological space. My understanding on this matter is limited but from my crude understanding of topology this is in fact wrong as matrices generalize to well beyond consisting of a topology.

 

I should probably add that homomorphism was probably the right word . . . . .

[DJBruce]

I'm sorry DJBruce but is homeomorphism the proper word or should you not be using homomorphism? I'm not so sure a matrix itself can be considered a topological space. My understanding on this matter is limited but from my crude understanding of topology this is in fact wrong as matrices generalize to well beyond consisting of a topology.

 

I should probably add that homomorphism was probably the right word . . . . .

 

Certainly there is a homomorphism from [latex]M_{n\times n}(\mathbb{C})[/latex] to [latex]M_{2n\times 2n}(\mathbb{R})[/latex], however, what I was referring to was the fact that you can think of [latex]M_{n\times n}(\mathbb{R}) [/latex] as a subset of [latex]\mathbb{R}^{2n}[/latex], and so we can consider it as a topological space. In fact many matrix groups such as [latex]GL_{n}(\mathbb{R})[/latex] have the "special" property of also having differential structures that work with the group structure aka Lie Group.

 

However, none of this theoretical stuff is probably strictly needed for Axioms problem. All they really need to do is multiple two complex numbers, and figure out how to write a matrix such that the matrix multiplication corresponds to this complex multiplication, and from their just generalize.

Edited May 29, 2012 by DJBruce

[Bignose]

I am just unsure if it is possible to input complex numbers in a matrix for the calculator to solve. I have lost my manual so thanks.

 

you do realize that Pixel provided a link to a .pdf version of the manual for your calculator, don't you?

[doG]

Hey I just want to find out if anyone knows if it is possible to enter complex numbers into a matrix of a scientific calculator.

The TI-89 has that capability. There's an emulator here.

[Axioms]

you do realize that Pixel provided a link to a .pdf version of the manual for your calculator, don't you?

 

I did. I said thanks.

 

No idea about whether or not your calculator can handle complex matrices. However, since there is a natural homeomorphism from to , and so also a nice homeomorphism from to , you can just use real matrices to try and solve your system.

 

It is simpler just to solve by hand but thanks anyway. I'm not sure if it would work because I'm shifting between a time domain and a phase domain constantly. Some of the numbers would be in a different domain and out of phase. I used a simple example to see if anyone knew if the matrix could be calculated on the calculator. I'd have then tried to apply the logic to my problem to see if it would be simpler than just working out what is needed.

 

The TI-89 has that capability. There's an emulator here.

 

Thanks.

[Greg H.]

The TI-92 could do this as well, IIRC. You can get an emulator for that from here: http://www.ticalc.org/basics/calculators/ti-92.html