Please help with this quadratic equation

Hello everyone so i am trying to solve this equation in matlab:

X-(abs(X))^2 = -j0.4

how do I do this? i always get errors doesn't matter which method I tried.

TYVM

[Amit]

what is j?

[jason]

j is the symbol for imaginary part of a complex number

Answer 1

[Mischa Kim]

Use

syms X
solve(X - (abs(X))^2 + i*0.4)

Of course, you can also use j instead of i.

[jason]

so whether the absolute function is present or not makes no difference to the result?

[Mischa Kim]

Right you are. Misread. I fixed it above.

Answer 2

[Roger Stafford]

You hardly need matlab to solve that problem. Rewrite it as:

 z - abs(z)^2 = -j*.4

where z = x + j*y with x and y being the real and imaginary parts of z. This can be rewritten:

 x + j*y - (x^2+y^2) = -.4*j

Now equate the real parts and imaginary parts of this equation:

 y = -.4
 x - x^2 - y^2 = x - x^2 - .16 = 0

From high school math there are two solutions to the second equation:

 x = (1 +/- sqrt(1-4*.16))/2 = .8 or .2

Thus the two solutions are:

 z = .8 - .4*j
 z = .2 - .4*j