Square Roots of Complex Numbers (CAS)

04232016, 09:12 PM
Post: #1




Square Roots of Complex Numbers (CAS)
It is great that expressions like sqrt(2^i) don't freeze up any more with the new update. And simply entering sqrt(i) will stay in the CAS, symbolic realm as (1+i)/sqrt(2), which is fine.
However, entering something like sqrt(1+i) will get approximated right away. If the user wants to approximate this expression, he/she can use Home, or press ~ in CAS   but it doesn't make any sense to have, for certain symbolic expressions, a numerical approximation forced on the user. For example, 3root(1+i) at least gets rewritten as exp(1/3*LN(1+i)). I know there is an issue with C++ exceptions (if I remember right)   I was only hoping that this might have been resolved by now. 

04232016, 10:15 PM
Post: #2




RE: Square Roots of Complex Numbers (CAS)
Would it be better displayed as 2^(1/4)*e^(i*π/8), or 4√ 2 *e^(i*π/8)? What alternate form would be most preferable? The [a b/c] key toggles between approx and exact modes, for a couple more options.


04232016, 10:52 PM
Post: #3




RE: Square Roots of Complex Numbers (CAS)
My point is, in CAS, just leave the expression alone
sqrt(1+i) > sqrt(1+i) Don't do any numerical evaluation! If the user wants to do that, they can do approx(), or work in Home. Sorry if that wasn't clear in the original post. 

04232016, 11:21 PM
Post: #4




RE: Square Roots of Complex Numbers (CAS)
Your post was probably clear enough, I'm just a little slow on the uptake! I was thinking you wanted further expression of the square root. Keeping it in the function form, makes it literally easier to read, and most of the alternate forms don't.


04232016, 11:46 PM
Post: #5




RE: Square Roots of Complex Numbers (CAS)
Yes, exactly! We're on the same page.
And look at sqrt(2^i) > sqrt(2^i), so that is what I would expect from a CAS. Now that symbolic expression can be used again in subsequent symbolic manipulations, whereas the forced, numerical output from sqrt(1+i) is worthless (in a symbolic reuse sense). 

04242016, 06:06 AM
Post: #6




RE: Square Roots of Complex Numbers (CAS)
The OS did not change with the new firmware...


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