1. ## Short question about trigonometry notation

I attatched a file but the problem to solve was to set $\displaystyle z+\overline{z}=1$ in a trigonometry notation
did I do it right?

Extra question: (another problem) the next problem is to set $\displaystyle z-\overline{z}=1$ in a trigonometry notation if someone could give me a hint how to solve that.

2. Originally Posted by hlolli
I attatched a file but the problem to solve was to set $\displaystyle z+\overline{z}=1$ in a trigonometry notation
did I do it right?

Extra question: (another problem) the next problem is to set $\displaystyle z-\overline{z}=1$ in a trigonometry notation if someone could give me a hint how to solve that.
Put $\displaystyle z=re^{i\theta}$ where $\displaystyle r=|z|$ and $\displaystyle \cos(\theta)=\text{re}(z)/|z|$ and $\displaystyle \sin(\theta)=\text{im}(z)/|z|$, then:

$\displaystyle z+\overline{z}=re^{i\theta} + re^{-i\theta}=2r\cos(\theta)$

or:

$\displaystyle z+\overline{z}=2|z|\cos(\text{arg}(z))$

CB

3. thanks for this, but can you tell me in words how I should write the picture for