Complex Numbers.

[axrw]

I feel a little stupid with this one, but...

z = a + bi and z` = a - bi

the conjugate of z is supposed to have a little line over the z instead, but whatever.

1. Find a general expression for 1/z.

I don't really get what they are looking for. It's a even numbered problem so the answer isn't in the back. What is a general expression supposed to be? Is it:

(a - bi)/(a^2 + b^2) ?

2. Solve z + 6z` = 7 for z.

Again, even numbered problem, but I'm guessing they don't want z = 7 - 6z` but I'm not quite sure how to proceed.

Thanks for any help.

 

[pka]

\(\displaystyle \L \frac{1}{z} = \frac{{\bar z}}{{\left| z \right|^2 }}\)