1. Вычислите: а) (2-3i)+(i+1)б) (2-3i)+(-1-i)в) (2-3i)-(i+1)г) (i+1)-(-1-i)д) (2-3i)x(i+1)е) (-1-i)x(i+1)2. Вычислите: a)

1. а) (2 - 3i) + (i + 1) = 2 - 3i + i + 1 = (2 + 1) + (-3i + i) = 3 + (-2i) = 3 - 2i.

б) (2 - 3i) + (-1 - i) = 2 - 3i - 1 - i = (2 - 1) + (-3i - i) = 1 + (-4i) = 1 - 4i.

в) (2 - 3i) - (i + 1) = 2 - 3i - i - 1 = (2 - 1) + (-3i - i) = 1 + (-4i) = 1 - 4i.

г) (i + 1) - (-1 - i) = i +1 + 1 + i = (1 + 1) + (i + i) = 2 + 2i.

д) (2 - 3i) * (i + 1) = 2 * i + 2 * 1 - 3i * i - 3i * 1 = 2i + 2 - 3i^2 - 3i = 2 - 3i^2 + (2i - 3i) = 2 - 3i^2 + (-i) = 2 - 3i^2 - i.

е) (-1 - i) * (i + 1) =  -1 * i - 1 * 1 - i * i - i * 1 = -i - 1 - i^2 - i = -1 - i^2 + (-i - i) = -1 - i^2 + (-2i) = -1 - i^2 - 2i.

2. a) (2 - i)(2 + i) - (3 - 2i) + 7 = 4 - 4i + i^2 - 3 + 2i + 7 = i^2 + (-4i + 2i) + (4 - 3 + 7) = i^2 + (-2i) + 8 = i^2 + -2i + 8.

б) (1+i)^4 = (1+i) * (1+i) * (1+i) * (1+i) = (1 + i + i + i^2) * (1 + i + i + i^2) = (1 + 2i + i^2) * (1 + 2i + i^2) = 1 + 2i + i^2 + 2i + 4i^2 + 2i^3 + i^2 + 2i^3 + i^4 = 1 + (2i + 2i) + (i^2 + 4i^2 + i^2) + (2i^3 + 2i^3) + i^4 = 1 + 4i +6i^2 + 4i^3 + i^4.