Question

determinati |z| si z compus daca

z = $\frac{1+4i}{1+7i}$

Answer 1

$z= \frac{(1+4i)(1-7i)}{(1+7i)(1-7i)}= \frac{1-7i+4i+28}{1+49}= \frac{29}{50}- \frac{3}{50}i \\ IzI= \sqrt{( \frac{29}{50})^2+( \frac{3}{50})^2 } = \sqrt{ \frac{850}{2500} } = \sqrt{ \frac{17}{50} }$