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- Nov 12th 2008, 12:02 PMdef77Complex numbers help
tt

- Nov 12th 2008, 12:55 PMPlato
I am not sure what the question says.

However, the following is true.

$\displaystyle \frac{1}{z} = \frac{1}{{z_1 }} + \frac{1}

{{z_2 }} + \frac{1}{{z_3 }} \Leftrightarrow \quad \frac{{\overline z }}

{{\left| z \right|^2 }} = \frac{{\overline {z_1 } }}

{{\left| {z_1 } \right|^2 }} + \frac{{\overline {z_2 } }}

{{\left| {z_2 } \right|^2 }} + \frac{{\overline {z_3 } }}

{{\left| {z_3 } \right|^2 }}$

That makes finding the real and imaginary parts easy. - Nov 12th 2008, 12:57 PMdef77
tt

- Nov 12th 2008, 01:06 PMPlato
You do know about the conjugate of a complex number don’t you?

$\displaystyle \overline {\left( {x + iy} \right)} = x - iy$

$\displaystyle \left| {iw} \right| = \left| i \right|\left| w \right| = \left| w \right|$ - Nov 12th 2008, 01:12 PMdef77
- Nov 12th 2008, 01:22 PMPlato
- Nov 12th 2008, 01:39 PMdef77
great, so if '1/iw' is that, then it can be flipped over to give me 'iw'. what im worrying about is that each of these (x^2 + y^2) are different values, i seem a wee bit out of my depth and i'll ask my professors tommorow see what they think, but i'll troop on for a while, see if i can make some progress on this. thanks for all the help so far, i'm starting to see the problem in context

- Nov 12th 2008, 02:13 PMPlato
- Nov 14th 2008, 05:41 AMgeo3
I thought I understood complex numbers and had a go at this qu but I cannot get a correct answer for the conjugate/ modulus of z3. Does the conjugate of 1/iw = -1/w and the modulus = 1/w ??? I have confused myself and now want to know how to do it!