maratoolHP 15C online: complex numbers, SOLVE and integrals
Do complex arithmetic, find a root and take a definite integral on a real HP 15C keyboard, with keystrokes you can copy.
HP sold the 15C from 1982 to 1989, and used ones still go for collector prices. I get why: it fits in a shirt pocket and does complex math, matrices, root finding and integration, all of it programmable. The HP 15C calculator online puts the whole keyboard in your browser. Every keystroke sequence below was run on it.
How it works
- Click the calculator once so it takes your keyboard.
- Key a number, press ENTER, key the next number, then press the operation.
- Read the result on the display and check the stack panel when you want to see Y, Z and T.
Complex numbers
The 15C keeps a second, imaginary stack alongside the normal one. To enter 3 + 4i, key the real part, ENTER, the imaginary part, then press f I:
3 ENTER 4 f I
The display shows 3.00 and the C annunciator comes on, which means complex mode is active and X now holds a complex number. Only the real part is shown. Press f (i) to look at the imaginary part.
From here most functions just work on the whole number. Press g →P and the display reads 5.00, the magnitude. Press f (i) and you get 53.13, the angle in degrees. Switch to radians with g RAD first if that's what your homework wants.
Finding a root with SOLVE
SOLVE needs the function written as a short program. For x² − 2 = 0, switch to program mode, key the function under label A, and switch back:
g P/R f LBL A g x² 2 − g RTN g P/R
When SOLVE calls the program, x is already sitting in X, so the program only has to square it and subtract 2. Now give it two guesses and run it:
1 ENTER 2 f SOLVE A
A second later the display shows 1.41, the square root of 2 at the default two decimals. If SOLVE can't find a sign change near your guesses it stops with Error 8. Move the guesses and try again.
A definite integral
Integration uses the same kind of program, so label A is ready to go. Put the lower limit in Y and the upper limit in X, then press f ∫xy and the label:
0 ENTER 3 f ∫xy A
The result is 3.00, which matches the textbook answer: x³/3 − 2x from 0 to 3 is 9 − 6. The 15C works out how many samples it needs from the display format, so a setting like FIX 2 finishes fast and FIX 9 takes longer but carries more correct digits.
Matrices, memory and the keyboard
Matrices A to E are sized with f DIM and filled with STO in user mode. They draw from the same memory pool as programs and registers, so a big matrix leaves less room for program steps. Owners of the original spent years juggling that, and you will too if you push it.
Once the calculator has focus you can type instead of clicking: digits, operators, Enter, f and g for the shifts, and A to E for the five keys of the top row. Keyboard Shortcuts under the calculator shows the full map. The memory survives a closed tab, and Save memory writes it to a file you can load anywhere else.