If x=3+4j is a root of x^2+ax+b=0, find the real numbers a and b.
For a quadratic equation with real coefficients complex roots are found as conjugate pairs. As the equation x^2 + ax + b = 0 has x = 3 + 4j as a root the other root is 3 - 4j
x^2 + ax + b = (x - (3 + 4j))(x - (3 - 4j))
=> x^2 + ax + b = (x^2 - x*6 + 9 + 16)
=> a = -6 and b = 25
The required values are a = -6 and b = 25