Final answer:
None of the given quadratic equations have two complex solutions.
Step-by-step explanation:
A quadratic equation has two complex solutions if the discriminant, b² - 4ac, is negative. Let's check each quadratic equation to see which ones have two complex solutions:
a) y = 2(x - 4)² + 5
The discriminant is 0, so it has two equal real solutions. Not a complex solution.
b) y = -2x + 16x - 37
The discriminant is positive, so it has two real and distinct solutions. Not a complex solution.
c) y = -5(x² - 3)
The discriminant is 0, so it has two equal real solutions. Not a complex solution.
d) y = -x² + 4x - 5
The discriminant is positive, so it has two real and distinct solutions. Not a complex solution.
e) y = -4(x + 2)² - 3
The discriminant is 0, so it has two equal real solutions. Not a complex solution.
Therefore, none of the given quadratic equations have two complex solutions. The correct answer is none of the above.