To find the roots of the equation x² + 8x + 25 = 0 in simplest a + bi form, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax² + bx + c = 0, the roots are given by:
\[ x = \frac{{-b \pm \sqrt{{b² - 4ac}}}}{2a} \]
In the given equation x² + 8x + 25 = 0, we have a = 1, b = 8, and c = 25. Plugging these values into the quadratic formula, we get:
\[ x = \frac{{-8 \pm \sqrt{{8² - 4*1*25}}}}{2*1} \]
\[ x = \frac{{-8 \pm \sqrt{{64 - 100}}}}{2} \]
\[ x = \frac{{-8 \pm \sqrt{{-36}}}}{2} \]
Since the square root of -36 is √(-36) = 6i (where i is the imaginary unit), the roots of the equation in simplest a + bi form are:
\[ x = \frac{{-8 + 6i}}{2} \] and \[ x = \frac{{-8 - 6i}}{2} \]
Simplifying these expressions, we get:
\[ x = -4 + 3i \] and \[ x = -4 - 3i \]
Therefore, the roots of the equation x² + 8x + 25 = 0 in simplest a + bi form are -4 + 3i and -4 - 3i.
