equation with complex number

[Jean-Patrick Pommier]

Hi,
Is it possible to solve equation with complex variable such 1/z=1+i?

I try without success:

show(solve(1/z==i,z))

 which returns

 [] (-i waited).

I didn't succeed well with:

z/conjugate(z)=z which is z0=1

I try also:

z=1+i
abs(z)=sqrt(2)

but arg(z) gives  0.785398163397
How to get the symbolic value  pi/4?

Thank you
Jean-Patrick

[David Joyner]

This is a question for sage-support, which I am ccing.

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[Štěpán Starosta]

Hi,

you need to tell sage to work with complex numbers. One way to do it:

var('z',domain=CC)
show(solve(1/z==i,z))

returns

[z=(-i)]

As for an argument of a complex number, I don't know. arg apparently
gives a numerical value, I don't know whether there is an algorithm to
do it symbolically for any complex number.

Stepan

On 9 pro, 11:04, Jean-Patrick Pommier <jeanpatrick.pomm...@gmail.com>
wrote: