Solve a system

Stu
15 ●3

Why this command doesn't give me any solution :

 solve([2*x+y==0,x-2*y==1],x)

I suppose because, there is an unique solution and x doesn't depend on y.

Now I would like to know when we solve an equation such that $$f(z)= 0\iff Re(x)+iIm(x)=0 $$ with $z=x+iy$ and $f(z)=5z-i\overline{z}^2+3+2i$

real(x)=-2*x*y + 5*x + 3
im(x) = -x^2 + y^2 + 5*y + 2
solve([real(x)==0, im(x)==0], x)

Is this command the right one to solve this problem ?

1 Answer

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calc314
4191 ●22 ●48 ●113

For the first solve question, you need to specify that you are solving for x and y.

solve([2*x+y==0,x-2*y==1],[x,y])

For the second question, you can do the following:

var('x y')
assume(x,'real')
assume(y,'real')
z=x+i*y
f=5*z-i*conjugate(z)^2+3+2*i
solve([f.real(),f.imag()],[x,y])

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Asked: 2018-05-04 18:27:50 +0100

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Last updated: May 04 '18