# Complex numbers help

• Oct 21st 2012, 01:19 PM
Benja303
Complex numbers help
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..
• Oct 21st 2012, 01:30 PM
Plato
Re: Complex numbers help
Quote:

Originally Posted by Benja303
I need help with numbers 11 and 12 in the attachted document.

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

#12 $\displaystyle z=\frac{(3-4i)(2+i)}{5}-i$
• Oct 21st 2012, 01:33 PM
Benja303
Re: Complex numbers help
I'm completely lost, please explain what you have here
• Oct 21st 2012, 02:21 PM
Plato
Re: Complex numbers help
Quote:

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: $\displaystyle \frac{1}{z} = \frac{{\overline z }}{{\left| z \right|^2 }}$.

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

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