Question

Даны комплексные числа z1 = 5 – 3i, z2 = 3 + 6i. найти сумму, произведение и частное этих чисел.

Answer 1

z1+z2=8+3i

z1-z2=2-9i

z1*z2=15+30i-9i-18i^2=33+21i

z1/z2=(5-3i)(3-6i)/(3+6i)(3-6i)=(15-30i-9i-18)/9+36=-3-39i/45=-1/15 -13i/15

Answer 2

$z_1 = 5 - 3i, z_2 = 3 + 6i\\\\ 1) z_1 + z_2 = 8 + 3i\\\\ (a_1 + ib_1 + a_2 + ib_2 = (a_1 + a_2) + i(b_1+ b_2))\\\\ 2) z_1*z_2 = (5 - 3i)(3 + 6i) =\\ 15 + 30i - 9i - 18i^2 =15 + 30i - 9i + 18 = 33 + 21i\\\\ 3) z_1/z_2 = (5-3i)/(3+6i) [| * 3 - 6i]=\\ (5-3i)(3-6i)/(3+6i)(3-6i) =\\ (15-30i -9i-18)/(9 -18i+18i+36) =\\ (-3-39i)/(45) = (-1/15) - (13/15)i$