Using the sum and product of roots: k = 1*4 = 4, and sum = 1 + 4 = 5, thus k = 7.

The discriminant must be greater than zero: 5² - 4*1*k > 0, thus k < 25.

Using the product of roots: q = 1 * 4 = 4.

Using the sum of roots (-3 + -4 = -7) and product of roots (-3*-4 = 12), we find k = 12.

Using the product of roots, k = 1*6 = 6.

Using the sum of roots (-3 + -4 = -7) and product of roots (-3*-4 = 12), we find p = 12.

Using the product of roots: p = (-3)(-4) = 12.

Using the product of roots: p = (-3)(-4) = 12.

The sum of the roots is 0 (m = 0) and the product is -1 (n = 1).

Using the sum of the roots: p = -(3 + 4) = -7.

The sum of the roots is -p = 3 + 4 = 7, hence p = -7.

Using the sum of roots formula, p = -(3 + (-2)) = -1, hence p = -1.

The product of the roots gives p = 2 * 4 = 8.

The possible outcomes are HH, HT, TH, TT. The outcomes with at least one tail are HT, TH, TT (3 outcomes). So, the probability is 3/4.

Possible combinations for sum 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) = 6 combinations. Total outcomes = 36. Probability = 6/36 = 1/6.

The complement A' consists of all elements in U that are not in A. Therefore, A' = {3, 4, 5}.

Substituting x = 5, we get 2(5) + 3 = 10 + 3 = 13.

|z| = √((-2)^2 + (2)^2) = √(4 + 4) = √8 = 2√2.

z^2 = (1 + i)^2 = 1^2 + 2(1)(i) + i^2 = 1 + 2i - 1 = 2i.

z² = (1 + i)² = 1² + 2(1)(i) + i² = 1 + 2i - 1 = 2i.

The argument is given by tan^(-1)(√3/1) = π/3.

|z|^2 = (2^2 + 2^2) = 4 + 4 = 8.

The conjugate of z = 2 - 3i is 2 + 3i.

The imaginary part of the complex number z = 3 + 4i is 4.

z + z* = (3 + 4i) + (3 - 4i) = 6.

z + z̅ = (3 + 4i) + (3 - 4i) = 6.

|z|^2 = 3^2 + 4^2 = 9 + 16 = 25.

The real part of the complex number z = 4 + 3i is 4.

The argument of z = 5 + 12i is given by arctan(12/5).

The imaginary part of the complex number z = 5 + 12i is 12.