http://img522.imageshack.us/img522/773/complex3xr8.png

How would you go about showing this?

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- Dec 14th 2008, 09:58 AMHariscomplex numbers problem
http://img522.imageshack.us/img522/773/complex3xr8.png

How would you go about showing this? - Dec 14th 2008, 10:12 AMPlato
Just multiply and collect terms: $\displaystyle \left[ {\left( {a + bi} \right)+\left( {c + di} \right)} \right]\left[ {\left( {a - bi} \right)+\left( {c - di} \right)} \right]$

- Dec 14th 2008, 10:14 AMMoo
Hello,

You can do it in two ways.

1st :

Write z and w with their real and imaginary parts and expand the LHS

2nd :

Use these rules :

$\displaystyle z\bar z=|z|^2$ for any complex number

$\displaystyle z+\bar z=2 \ \Re(z)$

$\displaystyle \bar z+\bar w=\overline{z+w}$

and then expand the LHS

There is another rule, but you don't need it here :

$\displaystyle z-\bar z=2 \ \Im(z)$