1. (3 + 5i) + (7 - 2i) = 3 + 7 + 5i - 2i = 10 + 3i
(-2 + 3i) - (4 + 2i) = -2 + 3i - 4 - 2i = -6 + i
(6 + 2i) + (5 + 3i) = 6 + 5 + 2i + 3i = 11 + 5i
(-3 - 5i) - (-7 - 2i) = -3 + 7 - 5i + 2i = 4 - 3i
2. (2 + 3i)(5 - 7i) = 10 - 14i + 15i - 21i² = 10 + i + 21 = 31 + i
(6 + 4i)(5 + 2i) = 30 + 12i + 20i + 8i² = 30 + 32i - 8 = 22 + 32i
(2 - 3i)(-5i) = -10i + 15i² = -15 - 10i
3. (2 + 3i)² = 4 + 12i + 9i²= 4 - 9 + 12i = 12i - 5
(3 - 5i)² = 9 - 30i + 25i² = 9 - 25 - 30i = -16 - 30i
(5 + 3i)³ = (5 + 3i)²(5 + 3i) = (25 + 30i + 9i²)(5 + 3i) = (25 - 9 + 30i)(5 + 3i) =
= (16 + 30i)(5 + 3i) = 80 + 48i + 150i + 90i² = 80 + 198i - 90 = -10 + 198i
4. 5i/(3 + 2i) = 5i(3 - 2i)/(3 + 2i)(3 - 2i) = (15i - 10i²)/(9 - 4i²) = (10 + 15i)/(13)=
= 10/13 + 15i/13
(2 - 3i)/(5 + 2i) = (2 - 3i)(5 - 2i)/(5 + 2i)(5 - 2i) = (10 - 4i - 15i + 6i²)/(25 - 4i²) =
= (10 - 6 - 19i)/(25 + 4) = (4 - 19i)/29 = 4/29 - 19i/29
(5 - 7i)/(5 + 7i) = (5 - 7i)²/(5 + 7i)(5 - 7i) = (25 - 70i + 49i²)/(25 - 49i²) =
= (-24 - 70i)/74 = -12/37 - 35i/37
(6 - 7i)/i = i(6 - 7i)/i² = (6i - 7i²)/(-1) = (6i + 7)/(-1) = -7 - 6i