HOW TO INPUT IMAGINARY NUMBERS INTO A MATRIX - Texas Instruments TI-84 Plus Calculator

Sorry, you cannot do that. If matrix is small split it in imaginary part and real part . This will double the dimensions. But this family of calculators you can have matrices with dimensions at most equal to three. Do the calculation by hand.

The 30XIIs doesn't deal with complex numbers directly. You can separate the real and imaginary parts and deal with them separately.

The 30Xa doesn't work with complex numbers. You'll have to work with the real and imaginary components separately, just like they taught you in class.

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.

This calculator can do simply algebra with complex numbers-addition, subtractions, multiplications, extract the imaginary and real parts- but not much else. Sorry, calculating exponentials or complex numbers is not within its capabilities.

Real Numbers are just numbers like: 1 12.38 -0.8625 3/4 ?2 1998 In fact:

Nearly any number you can think of is a Real Number
Real Numbers include: Whole Numbers (like 1,2,3,4, etc) Rational Numbers (like 3/4, 0.125, 0.333..., 1.1, etc ) Irrational Numbers (like ?, ?3, etc )

Real Numbers can also be positive, negative or zero.
So ... what is NOT a Real Number? ?-1 (the square root of minus 1) is not a Real Number, it is an Imaginary Number Infinity is not a Real Number And there are also some special numbers that mathematicians play with that are not Real Numbers
Why are they called "Real" Numbers?

Because they are not Imaginary Numbers.
The Real Numbers did not have a name before Imaginary Numbers were thought of. They got called "Real" because they were not Imaginary. That is the actual answer!
The Real Number Line The Real Number Line is like an actual geometric line.
A point is chosen on the line to be the "origin", points to the right will be positive, and points to the left will be negative.

A distance is chosen to be "1", and the whole numbers can then be marked off: {1,2,3,...), and also in the negative direction: {-1,-2,-3, ...}
Any point on the line is a Real Number:

• The numbers could be rational (like 20/9)
• or irrational (like ?)

But you won't find Infinity, or an Imaginary Number.
Real does not mean they are in the real world They are not called "Real" because they show the value of something real.
In mathematics we like our numbers pure, if we write 0.5 we mean exactly half, but in the real world half may not be exact (try cutting an apple exactly in half).

It is just a matter of being in EXACT mode. To set your calculator in EXACT mode here's the key sequence. Press [MODE] [F3] [Up Arrow] [Up Arrow] [Right Arrow] [2] [ENTER]. Now when your in the Matrix Editor you can input your numbers in decimal form and, they will be automatically be converted to a fractional format. Pictured below is a matrix that was entered using decimal numbers and, was converted into factional form. Notice at the bottom of the screen the calculator is in EXACT mode.


Here's the same matrix in the HOME screen.



Next is the same matrix converted back to decimal numbers. Notice at the bottom of the screen the calculator is in APPROX mode.



And of course when I turn the calculator back to EXACT mode and, Re-ENTER the decimal formatted matrix in the HOME screen the fractional formatted matrix reappears.

You can use the propFrac( command but, having in the EXACT mode setting works better.

Turn calculator ON.
If you see no icons, press [MENU] key.
Use Arrows to focus on RUN and press [EXE]
Press [OPTN]
Among the TABS that appear at the bottom of screen you have CPLX.
Press [F3] to activate it.
The menu TABS that are displayed allow you manipulate complex numbers:
F1 :i imaginary unit i
F2: Abs takes the absolute value of a complex number.
F3:Arg, gives the argument (angle the complex number makes with the positive X-Axis)
F4: Conj calculates the Conjugate of a number.
F5: ReP extracts the Real part
F6:Imp extracts the Imaginary part.

For other operations use the operation keys [Plus] [MINUS] [*][/] [X^2] [Square root]. Be careful using the universal power key or the xroot key as it may lead to a Memory error.

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.

Press MODE and select one of the two complex modes.