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+--- Thread: Square Roots of Complex Numbers (CAS) (/thread-6119.html)
Square Roots of Complex Numbers (CAS) - Helge Gabert - 04-23-2016 09:12 PM
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 re-written 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.
RE: Square Roots of Complex Numbers (CAS) - DrD - 04-23-2016 10:15 PM
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.
RE: Square Roots of Complex Numbers (CAS) - Helge Gabert - 04-23-2016 10:52 PM
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.
RE: Square Roots of Complex Numbers (CAS) - DrD - 04-23-2016 11:21 PM
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.
RE: Square Roots of Complex Numbers (CAS) - Helge Gabert - 04-23-2016 11:46 PM
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 re-use sense).
RE: Square Roots of Complex Numbers (CAS) - parisse - 04-24-2016 06:06 AM
The OS did not change with the new firmware...