Question

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

Answer 1

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

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