complex numbers in polar form on Wolfram Alpha

[sobriquet]

Hi.

Am I overlooking something or is it not possible to convert complex numbers
from rectangular to polar form on Wolfram Alpha?

https://www.wolframalpha.com/examples/mathematics/numbers/complex-numbers/

I know how to do it manually, like a+ib would
be sqrt(a^2+b^2) ∠ arctan(b/a), but is there no convenient
formalism for this?

https://www.allaboutcircuits.com/textbook/alternating-current/chpt-2/polar-rectangular-notation/

[konyberg]

Type your complex number in rectangular form and wolfram alpha will show you polar form.
KON

[sobriquet]

But what if I have it in polar form and I want to see it in rectangular form?
Or what if I have two numbers in polar form and I want to do some calculations with them without converting them to rectangular form?

[konyberg]

Why don't you try it?
KON

[sobriquet]

I do, but Wolfram Alpha simply seems unable to handle complex numbers in polar form.

For instance, if I enter 2+3i, it will tell me that it's
r = sqrt(13) (radius), θ = (180 tan^(-1)(3/2))/π° (angle), but when I
enter that back as an input, it tells me it doesn't understand the input.

Normally, when Wolfram Alpha gives some kind of output, it usually able to understand it as an input as well so you can use the output of one computation as an input for another computation.

[sobriquet]

https://i.imgur.com/i57F8bl.png

I'd expect Wolfram Alpha to do something basic like being able to recognize a complex number in polar form, so I'm just wondering if there is some special trick to enter complex numbers in polar form (for instance if you want to convert a complex number from polar to rectangular form).

[konyberg]

http://reference.wolfram.com/language/ref/FromPolarCoordinates.html
KON

[sobriquet]

But that won't work on Wolfram Alpha. I guess it would work in Wolfram Mathematica.

[konyberg]

I am stuck also.
Sorry.
KON

[James Waldby]

On Sat, 18 Aug 2018 09:10:59 -0700, sobriquet wrote:
> On Saturday, August 18, 2018 at 5:47:51 PM UTC+2, sobriquet wrote:
>> On Saturday, August 18, 2018 at 5:14:25 PM UTC+2, konyberg wrote:
>> > lørdag 18. august 2018 11.34.14 UTC+2 skrev sobriquet følgende:
>> > > On Saturday, August 18, 2018 at 10:03:07 AM UTC+2, konyberg wrote:
>> > > > lørdag 18. august 2018 01.49.09 UTC+2 skrev sobriquet følgende:
>> > > > > Am I overlooking something or is it not possible to convert
>> > > > > complex numbers from rectangular to polar form on Wolfram
>> > > > > Alpha?
>> > > > > https://www.wolframalpha.com/examples/mathematics/numbers/
complex-numbers/
>> > > > > I know how to do it manually, like a+ib would be sqrt(a^2+b^2)
>> > > > > ∠ arctan(b/a), but is there no convenient formalism for this?

...

>> > > But what if I have it in polar form and I want to see it in
>> > > rectangular form?
>> > > Or what if I have two numbers in polar form and I want to do some
>> > > calculations with them without converting them to rectangular form?

...

>> For instance, if I enter 2+3i, it will tell me that it's r = sqrt(13)
>> (radius), θ = (180 tan^(-1)(3/2))/π° (angle), but when I enter that
>> back as an input, it tells me it doesn't understand the input.
>>
>> Normally, when Wolfram Alpha gives some kind of output, it usually able
>> to understand it as an input as well so you can use the output of one
>> computation as an input for another computation.
> https://i.imgur.com/i57F8bl.png
>
> I'd expect Wolfram Alpha to do something basic like being able to
> recognize a complex number in polar form, so I'm just wondering if there
> is some special trick to enter complex numbers in polar form (for
> instance if you want to convert a complex number from polar to
> rectangular form).

The Wolfram Alpha functions "FromPolarCoordinates — convert from {r,θ}
to {x,y}" and "ToPolarCoordinates — convert from {x,y} to {r,θ}" can do
the arithmetic for you. Also see AbsArg[c] which converts a complex
number to polar form. To get from a complex number a+bi to a tuple or
list form {a,b} ReIm[p+qi] returns {p,q}. To get from {p,q} to p+qi,
you could say {p,q}[[1]]+i{p,q}[[2]] . You could define user functions
to wrap some of this up more neatly; see
<http://reference.wolfram.com/language/tutorial/DefiningFunctions.html>

--
jiw

[sobriquet]

I think you must be confusing Wolfram Mathematica with Wolfram Alpha.
Wolfram Alpha doesn't seem to speak the Wolfram language.

https://i.imgur.com/Jie9X2t.png

[James Waldby]

On Sat, 18 Aug 2018 11:37:32 -0700, sobriquet wrote:
...

>> The Wolfram Alpha functions "FromPolarCoordinates — convert from {r,θ}
>> to {x,y}" and "ToPolarCoordinates — convert from {x,y} to {r,θ}" can do
>> the arithmetic for you. Also see AbsArg[c] which converts a complex
>> number to polar form. To get from a complex number a+bi to a tuple or
>> list form {a,b} ReIm[p+qi] returns {p,q}. To get from {p,q} to p+qi,
>> you could say {p,q}[[1]]+i{p,q}[[2]] . You could define user functions
>> to wrap some of this up more neatly; see
>> <http://reference.wolfram.com/language/tutorial/DefiningFunctions.html>

> I think you must be confusing Wolfram Mathematica with Wolfram Alpha.
> Wolfram Alpha doesn't seem to speak the Wolfram language.
> https://i.imgur.com/Jie9X2t.png

Click 'Open Code' in the input box so you can use Wolfram language.
Eg, on <http://www.wolframalpha.com/input/?i=3%2B4i> clicking Open
Code goes to a page at https://sandbox.open.wolframcloud.com on
which you can enter code. (Highlight most of what's there and press
delete to get it out of the way, then type stuff in and press the
right-pointing triangle to execute it.) (Use I instead of i there.)

--
jiw

[sobriquet]

Ah ok, yes, that way it works, but then you are in the Wolfram Cloud and no longer on Wolfram Alpha.

The interface of Wolfram Cloud looks exactly like Wolfram Mathematica.