If z is a complex number of unit modulus and argument [ ], then arg [( 1 + z 1 + z )] equa…

Question

If z is a complex number of unit modulus and argument $$\theta $$, then arg $$\left( {{{1 + z} \over {1 + \overline z }}} \right)$$ equals :

Accepted Answer

Given $$\,\,\,\,\left| z \right| = 1,\,\,\arg \,z = \theta $$

As we know, $$\,\,\,\,\overrightarrow z  = {1 \over z}$$

$$\therefore$$ $$\,\,\,\,\arg \left( {{{1 + z} \over {1 + \overrightarrow z }}} \right) = \arg \left( {{{1 + z} \over {1 + {1 \over z}}}} \right)$$

$$ = \arg \left( z \right) = \theta .$$

Solutions · 1