Question

Salut, am nevoie de ajutor la ex. 1.350C( explicatii pas cu pas , va rog)

Answer 1

$|z| = |z'| = 1 \\ \\ z\cdot \overline{z} = 1\\ z'\cdot \overline{z'} = 1\\ \\ w = \dfrac{z+z'}{1+zz'} \\\\w = \dfrac{\overline{z'}\overline{z}(z+z')}{\overline{z'}\overline{z}(1+zz')} = \dfrac{\overline{z'}+\overline{z}}{\overline{z'}\overline{z}+1}=\dfrac{\overline{z}+\overline{z'}}{1+\overline{z}\overline{z'}}=\overline{w}\\ \\ \\\Rightarrow w = \overline{w} \Rightarrow w\in \mathbb{R}$

=> a) corect