Complex Number Support (was: Re: 32SII -- well-said!) Message #16 Posted by Jeff O. on 7 Apr 2005, 12:50 p.m., in response to message #12 by Thomas Okken
Thomas,
I have made some suggestions directly to you, but for the benefit of others and to solicit opinions, I'll repeat them here. The way the 42S handles complex numbers is very good, by far the best of any hp calculator. However, if I could, I would enhance the way complex numbers are entered, displayed, and converted back and forth between rectangular and polar form. To make entry more natural, I propose that a key labelled "i" be included on the keyboard. This would be the label on the face of the key for the primary function, not a shifted function. When entering a complex number in rectangular form, one would merely key in the real part, then press "i" to terminate entry of the real part and begin entering the imaginary part. When done, you would press ENTER or any other operation as usual after keying in any number. Both the real and imaginary parts of the number would be displayed on one line in the display in the same way the 42S does it (NOT the way the 28, 48 and 49 display complex numbers). To key in a number in polar form, one would not need to switch to polar display mode. Either there would be a separate key, or the "i" key would have a shifted function, labelled with the angle symbol. To enter a number in polar form, you would merely enter the magnitude, then press the angle key (or shift "i"), then enter the angle. The number would be displayed on one line in the display in polar form, again exactly as the 42S does. Complex numbers in rectangular form and complex numbers in polar form would be allowed to exist in the stack and/or any memory registers at the same time. You could key in a rectangular form number, press enter, key in a polar form number, press multiply, divide, etc. and get your answer immediately with no worry about being in polar display mode or rectangular display mode. The answer would by default be displayed in the format of the number in the X register. As I see things, there would be no real need for "polar" or "rectangular" display modes. There should be keys with rectangular to polar and polar to rectangular conversion functions. (Please label them as ->R and ->P, not the ->phi,r and ->y,x labelling of the 33S.) These keys would function as they do on the 42S. If the displayed number is complex and displayed in polar form and you press the ->R key, it takes the two components, treats them as magnitude and angle and converts and displays them in rectangular form. If the displayed number is complex and displayed in rectangular form and you press the ->P key, it takes the two components, treats them as real and imaginary components and converts and displays them in polar form. (If you try to convert a polar form number to polar form or convert a rectangular form number to rectangular form, nothing would happen.) If the X-register contains a real number, it takes the numbers in the X and Y registers and converts and displays them accordingly. In a complex functions menu, there would be a global command to convert all numbers currently stored in the calculator to either polar or rectangular display. In this case, it would not alter numbers already in rectangular form when converting all to rectangular, and would not alter numbers already in polar form when converting to polar. As an alternative, the “mixed” display mode described above could be an optional mode, along with all polar and all rectangular. If rectangular and polar display modes are available, you could still enter a polar form number directly using the “angle” key when in rectangular mode. The number would be converted to rectangular form when you press ENTER. That summarizes my ideas on the perfect complex number support system. I will readily note that similar ideas were expressed by Karl Schneider in this post a while back. I think I had thought of having the “i” key and some of the other ideas before then, but I’ll be happy to share credit with Karl :-)
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