complex numbers problem

**Haris** · December 14th 2008, 09:58 AM

How would you go about showing this?

**Plato** · December 14th 2008, 10:12 AM

Just multiply and collect terms: $\left[ {\left( {a + bi} \right)+\left( {c + di} \right)} \right]\left[ {\left( {a - bi} \right)+\left( {c - di} \right)} \right]$

**Moo** · December 14th 2008, 10:14 AM

Hello,

Originally Posted by Haris

How would you go about showing this?

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 :
$z\bar z=|z|^2$ for any complex number
$z+\bar z=2 \ \Re(z)$
$\bar z+\bar w=\overline{z+w}$
and then expand the LHS

There is another rule, but you don't need it here :
$z-\bar z=2 \ \Im(z)$

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