Question

find the modulus of 1/1+i​

Answer 1

$z = \frac{1}{1 + \sqrt{ - 1} }$

$z = \frac{1 - \sqrt{ - 1} }{ {1}^{2} - {( \sqrt{ - 1}) }^{2} }$

$z = \frac{1 - \sqrt{ - 1} }{2}$

$\implies z = \frac{1}{2} - \frac{1}{2} i$

$\therefore |z| = \sqrt{( \frac{1}{2} ) ^{2} + {( \frac{1}{2} )}^{2} }$

$\underline{ |z| = \frac{ \sqrt{2} }{2} }$