Unit vector = (4/5, 3/5) where magnitude = √(4^2 + 3^2) = 5

Unit vector = (4/5, 3/5) since magnitude = 5.

Unit vector = v / |v| = (3, 4) / 5 = (0.6, 0.8)

Unit vector = A / |A| = (3, 4) / 5 = (0.6, 0.8).

Magnesium has a valency of 2, as it can lose two electrons.

Oxygen has a valency of 2, as it needs two electrons to complete its outer shell.

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

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

Using BODMAS: (2 + 3) = 5 and (4 - 1) = 3, so 5 × 3 = 15.

Using the binomial theorem, (2 + 3)^3 = 5^3 = 125.

Using the binomial theorem, (2 + 3)^3 = C(3,0)(2)^3 + C(3,1)(2)^2(3) + C(3,2)(2)(3)^2 + C(3,3)(3)^3 = 8 + 36 + 54 + 27 = 125.

Multiply numerator and denominator by the conjugate of the denominator: (2 + 3i)(1 - i) / (1 + i)(1 - i) = (2 - 2i + 3i + 3) / (1 + 1) = (5 + i) / 2 = 2.5 + 0.5i.

Using the difference of squares: (a + b)(a - b) = a² - b². Here, (2)² - (3i)² = 4 - (-9) = 4 + 9 = 13.

Using the binomial theorem, (2 - 3)^5 = (-1)^5 = -1.

(2x + 3)² = 4x² + 12x + 9 by expanding the square of a binomial.

Using the property of exponents, (2^3) * (2^2) = 2^(3+2) = 2^5.

Multiplying numerator and denominator by the conjugate of the denominator: (3 + 4i)(1 - i) / (1 + i)(1 - i) = (3 - 3i + 4i + 4) / 2 = (7 + i) / 2 = 2 + i.

(3 + 5) = 8 and (2 + 4) = 6, so 8 × 6 = 48.

(3 + 5) = 8 and (2 - 1) = 1, so 8 × 1 = 8.

(3 + 5) = 8 and (6 - 2) = 4, so 8 × 4 = 32.

(3 + 5) × 2 = 8 × 2 = 16.

3^3 = 27 and 2^3 = 8, so 27 - 8 = 19.

4^2 * 4^3 = 4^(2+3) = 4^5 = 1024

Calculating each term, we have 5^0 = 1, 5^1 = 5, and 5^2 = 25. Therefore, 1 + 5 + 25 = 31.

(a + b)² = a² + 2ab + b² by the expansion of the square of a binomial.

(x + 1)(x - 1) = x² - 1, which is the difference of squares.

Using the binomial theorem, (x + 1)^5 = C(5,0)(2)^5 + C(5,1)(2)^4 + C(5,2)(2)^3 + C(5,3)(2)^2 + C(5,4)(2)^1 + C(5,5)(2)^0 = 32 + 80 + 80 + 40 + 10 + 1 = 243.

Using the power of a power property, (x^2)^3 = x^(2*3) = x^6.

Multiplying three negative ones gives −1.

(−1)^3 = −1.