Square Roots of Complex Numbers (CAS)

[Helge Gabert]

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.

[DrD]

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.

[Helge Gabert]

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.

[DrD]

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.

[Helge Gabert]

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).

[parisse]

The OS did not change with the new firmware...