# Maxima, Minima complex function

1. May 22, 2010

### heinerL

Hey

my problem is that im 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?

2. May 22, 2010

### gabbagabbahey

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

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

3. May 22, 2010

### heinerL

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

4. May 22, 2010

### gabbagabbahey

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

5. May 22, 2010

### 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?

6. May 22, 2010

### 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