Question

найдите произведение и частное комплексных чисел: z1= 5-3i z2= -1-6i
z1*z2=?
z1:z2=?

Answer 1

z1*z2=13-27i

$\frac{z_1}{z_2}=\frac{33i+13}{37}$

Объяснение:

z1*z2=(5-3i)*(-1-6i)=-5+3i-30i+18i²=5-18-27i=-13-27i

$\frac{z_1}{z_2}=\frac{5-3i}{-1-6i}=\frac{5-3i}{-(1+6i)}=\frac{-1(5-3i)}{(1+6i)}=\frac{3i-5}{1+6i}=$

$=\frac{3i-5}{1+6i}=\frac{(3i-5)(1-6i)}{(1+6i)(1-6i)}=\frac{3i-5-18i^2+30i}{(1^2-36i^2)}=\frac{33i+13}{1+36}=\frac{33i+13}{37}$