Question

Calculați modulul numarului Z=9-2i/7+6i

Answer 1

$\frac{9-2i}{7+6i}= \frac{(9-2i)(7-6i)}{7^2-(6i)^2}= \frac{63-54i-14i-12}{49+36}= \frac{51-68i}{85}$
|z|= $\sqrt{ \frac{51^2}{85^2}+ \frac{68^2}{85^2} }= \sqrt{ \frac{2601+4624}{85^2} } = \frac{ \sqrt{7225} }{85} = \frac{85}{85} =1$