Question

помогите пж
$z1 = sqrt{2} - frac{i5}{4}$
$z = 3 - frac{i}{2}$
$frac{z1}{z2} = ?$

Answer 1

$z_1=sqrt{2}-idfrac{5}{4}medskip \ z_2=3-idfrac{1}{2} medskip \ dfrac{z_1}{z_2}=dfrac{sqrt{2}-ifrac{5}{4}}{3-ifrac{1}{2}}=dfrac{left(sqrt{2}-frac{5}{4}iright)left(3+frac{1}{2}iright)}{9+frac{1}{4}}=medskip\=dfrac{4left(3sqrt{2}+frac{5}{8}+ileft[frac{2sqrt{2}-15}{4}right]right)}{37}=dfrac{12sqrt{2}+2.5+ileft[frac{2sqrt{2}-15}{4}right]}{37}=medskip\=dfrac{12sqrt{2}+2.5}{37}+ileft(dfrac{2sqrt{2}-15}{148}right)$

Ответ. $dfrac{z_1}{z_2}=dfrac{12sqrt{2}+2.5}{37}+ileft(dfrac{2sqrt{2}-15}{148}right)$