# Caclulating Complex Number j Terms

#### SamR

Joined Mar 19, 2019
3,180
Yes, I can do it with a pencil and paper along with many other complex calculations. BUT Is there a calculator to aid with this? In particular TI-83, wxMaxima, WolframAlpha, etc? Thx.

Sam

#### WBahn

Joined Mar 31, 2012
26,398

Type something like (4+7i)*(3-9i) into the search field and hit enter.

#### SamR

Joined Mar 19, 2019
3,180
I've tried many sites by now after googling. j4 in most becomes j^4 and 4j gives error codes. TI's new Nspire 2019 model calculator handles both rectangular and polar but they are asking $170 for it now ($30 increase) with back to school boom going on. It also comes with a "student software package" that is an emulator for your pc and USB cable for xfr between other calcs or PC and charging the calc. Might just have to do it the old fashioned way for a while. Been mostly using TI-35 solar for many years and for e calculations the TI-83 which is big and heavy but then the new Nspire is big also.

#### SamR

Joined Mar 19, 2019
3,180
It appears that wxMaxima can do Complex rectangular and polar forms and conversions. I do not know enough about Maxima as of now. Lots to learn there about syntax.

EDIT: NVM I found it on Utube and my old TI-83 does it easily.

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#### crutschow

Joined Mar 14, 2008
26,735
My favorite, the old HP42s handles both the polar and rectangular form of complex numbers, and will return a complex number for the square-root of a negative number, which few calculators can do (below is the result for the square-root of -3).

Of course it uses RPN, which I much prefer over algebraic entry, since it seems more logical to me and you never need to use parenthesis, but it can take a little getting used to.

If interested, this website has a perfect virtual replica of it (looks and operates exactly like the real calculator) that can run on windows or your smart-phone.
I have it on my PC and my Android phone (my phone display then looks exactly like an HP42s calculator).
It's free, but I sent him a few bucks, since he obviously put in a great deal of work to so faithfully reproduce its look and operation.
Even the dot-matrix display looks identical to the real unit.
I use it all the time since my real HP42s gave up the ghost.

A really interesting function on it is the SOLVER.
You can program in an equation with several variables, put in values for all but one of the variables, and it will iteratively solve for the unknown.
For example, below shows the results for an equation I put in relating resistance, capacitance, and frequency (F = 1/2Pi*RC).
I arbitrarily put in a value of 1000 for R and 1e-6 for C.
Then pressing F gave me the answer of 159.15(Hz).
You can do that for any combination of variables, such as putting in C and F to find R, or R and F to find C.
Note that you can use any arbitrary alphanumeric label (up to 3 characters I think) for the variables in your equations.

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#### SamR

Joined Mar 19, 2019
3,180
My first "electronic slide-rule" was the TI SR-50 @ $150 which was much cheaper (less than half) than the HP35 @$350 & 45s @ $500. My dad paid$175 for his and six months later my brother bought his for 50. You could program 30-50 lines of code in it and save the program for often used calculations. Rechargeable battery packs didn't live long and were not cheap to replace. Still have my K&E Log Log Duplex Decilon and shudder every time I see it. I would take learning RPN (which I like) over the Slide-rule any day. #### DickCappels Joined Aug 21, 2008 7,155 The HP-35S calculators only seem to last a couple of years before the keyboard gets intermittent -been through a few over the years. Installed Free 42 (as crutschow mentioned) a while back on my iphone and like it a lot. And guess what? No keyboard problems! Thread Starter #### SamR Joined Mar 19, 2019 3,180 I have some kind of scientific calc on the phone, but I'm not much of a phone user especially with my bad eyes. #### crutschow Joined Mar 14, 2008 26,735 And I still have my old Dietzgen log-log somewhere (it uniquely had a micrometer type small screw at one end to align the slides) which would cost upwards of300 in today's prices.
I remember learning a technique to help with polar to rectangular conversion using the log-log scales.
I would have given a eye tooth for an HP-35 type calculator to use in school (well before they were available).
My first scientific was an HP-25, which were more reasonably priced, but wasn't as ergonomic as the 35.

#### WBahn

Joined Mar 31, 2012
26,398
I've tried many sites by now after googling. j4 in most becomes j^4 and 4j gives error codes. TI's new Nspire 2019 model calculator handles both rectangular and polar but they are asking $170 for it now ($30 increase) with back to school boom going on. It also comes with a "student software package" that is an emulator for your pc and USB cable for xfr between other calcs or PC and charging the calc. Might just have to do it the old fashioned way for a while. Been mostly using TI-35 solar for many years and for e calculations the TI-83 which is big and heavy but then the new Nspire is big also.
You don't go to any site, you use the Google search engine itself as the calculator.

Did you try the example I gave you?

Remember that the use of 'j' for sqrt(-1) is somewhat narrow and is a convention used by electronics folks because of the prevalent use of 'i' as a variable for current. Most of the world uses 'i' as the imaginary unit.

#### SamR

Joined Mar 19, 2019
3,180
the use of 'j' for sqrt(-1) is somewhat narrow
Yes, it does. I had to learn to use the i for imaginary instead of j even on the TI83. Thx!

It seems to be a bit of confusion. Grobb's states it as 2 + j3 and some others as 2 + 3j. All works the same even with the different syntax.

As a kid, I built an electronic slide rule using 3 logarithmic pots and a BFO. Dial-in the 2 numbers to multiply and twilt the third pot to null for the solution. Crude but kinda worked and not very accurate but a fun little build. I always felt like slide rule answeres were guesstimates and kept the CRC book of tables handy.

Don't remember the Dietzgen rule, It seems like they only sold Pickett or K&E in the bookstore. Never did like those bright yellow aluminum rules.

My dad always carried a 6" in his shirt pocket and when he finally sat for his PE exam (after almost 30 years) he was the only guy in the room still using a slide rule. After that was when he finally bought a calculator.

#### djsfantasi

Joined Apr 11, 2010
7,551
I've tried many sites by now after googling. j4 in most becomes j^4 and 4j gives error codes. TI's new Nspire 2019 model calculator handles both rectangular and polar but they are asking $170 for it now ($30 increase) with back to school boom going on. It also comes with a "student software package" that is an emulator for your pc and USB cable for xfr between other calcs or PC and charging the calc. Might just have to do it the old fashioned way for a while. Been mostly using TI-35 solar for many years and for e calculations the TI-83 which is big and heavy but then the new Nspire is big also.
It appears that Google uses the US convention for imaginary numbers. That is if you type
(3+4i)*1​
You get a solution. But if you were to type
(3+4j)*1​
It thinks it is an algebraic expression.

#### WBahn

Joined Mar 31, 2012
26,398
Yes, it does. I had to learn to use the i for imaginary instead of j even on the TI83. Thx!

It seems to be a bit of confusion. Grobb's states it as 2 + j3 and some others as 2 + 3j. All works the same even with the different syntax.
Since multiplication is commutative, j3 and 3j are equivalent. Particular software packages may impose constraints on the representation, such as requiring the imaginary unit as a prefix so that the tokenizer can recognize imaginary numbers.