Question

aflati partea imaginara a numarului Z=5+7i/5-7i

Answer 1

Răspuns:

Explicație pas cu pas:

$z=\dfrac{5+7i}{5-7i}= \dfrac{(5+7i)^2}{(5-7i)(5+7i)}=\dfrac{25+70i+49i^2}{25-49i^2}=\dfrac{25+49*(-1)+70i}{25-49*(-1)}=\dfrac{-24+70i}{74}=\dfrac{2(-12+35i)}{2*37}=\dfrac{-12+35i}{37}=-\dfrac{12}{37}+\dfrac{35}{37}i\\Deci~~Im~z=\dfrac{35}{37}.$