Final answer:
The complex solutions of the equation x²+3x+4=0 are x = (-3 + i√7) / 2 and x = (-3 - i√7) / 2.
Step-by-step explanation:
To find the complex solutions of the equation x²+3x+4=0, we can use the quadratic formula. For an equation of the form ax²+bx+c=0, the quadratic formula is: x = (-b ± √(b² - 4ac)) / (2a). In this case, a = 1, b = 3, and c = 4, so we have: x = (-3 ± √(3² - 4(1)(4))) / (2(1)). Solving this equation, we get x = (-3 ± √(-7)) / 2. Since the discriminant (√(-7)) is imaginary, the solutions are complex numbers. Therefore, the complex solutions to the equation are: x = (-3 + i√7) / 2 and x = (-3 - i√7) / 2.