Maxima, Minima complex function

[heinerL]

Hey

my problem is that I am unable to calculate the absolute value of the following function:

f(z)=\bar{z}(z-2)-2\Re z wherase z=x+iy

What i did was:

=|z|^2-2\bar{z}-2\Re z=x^2+y^2-2x+2iy-2x=x^2+y^2+2yi-4x

and how should i calculate the absoulte value of this function??

Because i should find all maxima and minima of |f(x)|, which is not so difficult, i hope after i got the abs()!

Can anyone help me?

 

[gabbagabbahey]

I don't think you are looking for the "absolute value", but rather the norm:

|a+ib|=\sqrt{a^2+b^2}

 

[heinerL]

yes, you're right, i mean the norm |a+ib|= \sqrt{a^2+b^2} but how should i proceed?

 

[gabbagabbahey]

Square the real and imaginary parts of your expression, add them together and take the square root of the result.

 

[heinerL]

you mean that:

\abs(x^2+y^2-4x+2iy)=\sqrt{(x^2+y^2-4x)^2+4y^2}

that (x^2+y^2-4x) is the real part and 2iy the imaginary part?

 

[Mentallic]

In a+ib, a is the real part and b is the imaginary part. That is, don't include the imaginary unit i in the imaginary part.

And yes, you're right