The quadratic formula can be used to find the complex roots of the equation P(z) = 0, where P(z) = x² + iz + 5/2. The quadratic formula is:
z = (-b ± √(b² - 4ac)) / 2a
where a, b, and c are the coefficients of the quadratic equation. In this case, a = 1, b = i, and c = 5/2.
Substituting these values into the quadratic formula, we get:
z = (-i ± √(i² - 4 * 1 * 5/2)) / 2 * 1
z = (-i ± √(-9/2)) / 2
z = (-i ± √(-9) / √2) / 2
z = (-i ± 3i / √2) / 2
z = (-i ± √2 * i) / 2
z = (-1 ± √2)i / 2
Therefore, the complex roots of the equation P(z) = 0 are:
z = (-1 + √2)i / 2
z = (-1 - √2)i / 2