Complex Numbers.

[axrw]

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

z = a + bi and z${\displaystyle =a-bitheconjugateofzis\supset posed\to haveali\le l\in eoverthez\in stead,butw\hat{e}ver.1.F\in da\ge \ne ral\exp ressionf\text{or}\frac{1}{z}.Idon\prime treally\ge tw\hat{t}heyarel\infty k\in gf\text{or}.It\prime saeven\nu mberedprob\le msotheanswerisn\prime t\in theback.W\hat{i}sa\ge \ne ral\exp ression\supset posed\to be?Isit:\frac{a-bi}{a^2+b^2}?2.Solvez+6z}$ = 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]

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