# Math Help - Complex numbers help

1. ## Complex numbers help

tt

2. I am not sure what the question says.
However, the following is true.
$\frac{1}{z} = \frac{1}{{z_1 }} + \frac{1}
{{z_2 }} + \frac{1}{{z_3 }} \Leftrightarrow \quad \frac{{\overline z }}
{{\left| z \right|^2 }} = \frac{{\overline {z_1 } }}
{{\left| {z_1 } \right|^2 }} + \frac{{\overline {z_2 } }}
{{\left| {z_2 } \right|^2 }} + \frac{{\overline {z_3 } }}
{{\left| {z_3 } \right|^2 }}$

That makes finding the real and imaginary parts easy.

3. tt

4. You do know about the conjugate of a complex number don’t you?
$\overline {\left( {x + iy} \right)} = x - iy$

$\left| {iw} \right| = \left| i \right|\left| w \right| = \left| w \right|$

5. Originally Posted by Plato
You do know about the conjugate of a complex number don’t you?
$\overline {\left( {x + iy} \right)} = x - iy$

yep, just doing my numerators, getting -1 - iw - 1/(iw) if i'm assuming x for the conjugate is 0, though i'm a bit iffy on whether the complex conjugate of 1/iw is -1/iw. next for the modulus of iw

6. Originally Posted by def77
yep, just doing my numerators, getting -1 - iw - 1/(iw) if i'm assuming x for the conjugate is 0, though i'm a bit iffy on whether the complex conjugate of 1/iw is -1/iw. next for the modulus of iw
$w = x + iy \Rightarrow \quad \left( {\frac{1}
{{iw}}} \right) = \frac{{\overline {iw} }}
{{\left| w \right|^2 }} = \frac{{ - y - ix}}
{{x^2 + y^2 }}$

7. Originally Posted by Plato
$w = x + iy \Rightarrow \quad \left( {\frac{1}
{{iw}}} \right) = \frac{{\overline {iw} }}
{{\left| w \right|^2 }} = \frac{{ - y - ix}}
{{x^2 + y^2 }}$
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

8. Originally Posted by def77
so if '1/iw' is that, then it can be flipped over to give me 'iw'.
NO!
$\mbox{Re}(iw) = - \mbox{Im}(w)\; \;\&\;\; \mbox{Im}(iw)=\mbox{Re}(w)$

9. 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!