Expanding gives x^2 + 4 = 5, so x^2 = 1, thus x = ±1.

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

The conjugate of a complex number a + bi is a - bi. Thus, the conjugate of 2 - 3i is 2 + 3i.

Multiplying z1 and z2: (1 + i)(2 - i) = 2 - i + 2i - 1 = 3 + i.

Using the quadratic formula x = [-b ± √(b^2 - 4ac)] / 2a, we find the roots are -2 ± i.

The argument of a complex number a + bi is given by tan^(-1)(b/a). Here, it is π since the point lies on the negative x-axis.

The modulus is calculated as √(3^2 + 4^2) = √(9 + 16) = √25 = 5.

The product of the roots of a quadratic equation ax^2 + bx + c = 0 is c/a. Here, c = 9 and a = 1, so the product is 9.

The sum of the roots of a quadratic equation ax^2 + bx + c = 0 is -b/a. Here, -3/1 = -3.

i^4 = (i^2)^2 = (-1)^2 = 1.