The coefficient of x^3 is C(6,3) * (2)^3 = 20 * 8 = 160.

The coefficient of x^3 is C(5,3) * (-1)^2 = 10.

The coefficient of x^3 is C(6,3) * (-1)^3 = 20 * (-1) = -20.

The coefficient of x^3 is C(5,3) * (-3)^2 = 10 * 9 = -90.

Using the binomial theorem, the coefficient of x^4 in (3x - 2)^6 is given by 6C4 * (3)^4 * (-2)^2 = 15 * 81 * 4 = 4860.

The coefficient of x^5 is C(8,5) = 56.

The coefficient of x^5 is C(8,5) * (3)^3 = 56 * 27 = 1512.

The coefficient of x^5 is C(7,5) * (-3)^2 = 21 * 9 = -1890.

The conjugate of z = 5 - 6i is z̅ = 5 + 6i.

The determinant of an upper triangular matrix is the product of its diagonal elements, which is 1.

The determinant is calculated as \( 3*4 - 2*1 = 12 - 2 = 10 \).

The determinant of the identity matrix is always 1.

The determinant is calculated as \( 2*4 - 1*3 = 8 - 3 = 5 \).

The determinant evaluates to 0.

Using the determinant formula, we find it equals 10.

The determinant is \( 2*4 - 3*1 = 8 - 3 = 5 \).

The determinant is given by the formula \( ad - bc \).

This is the identity matrix, and its determinant is 1.

The determinant evaluates to 0 as the third row can be expressed as a linear combination of the first two.

det = (1*5) - (2*3) = 5 - 6 = -1.

The characteristic polynomial is det(A - λI) = (2-λ)(2-λ) - 1 = λ^2 - 4λ + 3 = 0, giving eigenvalues 1 and 3.

The inverse of A is (1/det(A)) * adj(A) = (1/-2) * [[4, -2], [-3, 1]] = [[-2, 1]; [1.5, -0.5]].

The real part of z = 2 + 3i is 2.

The real part is 2 * cos(π/3) = 2 * 1/2 = 1.

The real part of z is 3.

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

The real part is 4 * cos(π/3) = 4 * 1/2 = 2.

The real part of z = 5 - 2i is 5.

2(x - 1) ≥ 3 => x - 1 ≥ 1.5 => x ≥ 2.5.

2x + 3 ≤ 5 => 2x ≤ 2 => x ≤ 1.