Complex numbers help

**Benja303** · October 21st 2012, 01:19 PM

I need help with numbers 11 and 12 in the attachted document.

I'm not trying to cheat because the answers are already given.. It's not marked work..

**Plato** · October 21st 2012, 01:30 PM

Originally Posted by Benja303

I need help with numbers 11 and 12 in the attachted document.

#11 $\frac{x}{2-i}=\frac{x(2+i)}{5}~\&~\frac{y}{1+3i}=\frac{y(1-3i)}{10}$

#12 $z=\frac{(3-4i)(2+i)}{5}-i$

**Benja303** · October 21st 2012, 01:33 PM

I'm completely lost, please explain what you have here

**Plato** · October 21st 2012, 02:21 PM

Originally Posted by Benja303

I'm completely lost, please explain what you have here

This is not a tutorial service.
Both of those questions turn on this fact: $\frac{1}{z} = \frac{{\overline z }}{{\left| z \right|^2 }}$ .

Example: $\frac{1}{3-4i}=\frac{3+4i}{25}$ .

If $(1+3i)z=2+i$ then $z=\frac{(2+1)(1-3i)}{10}$ .

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