Final answer:
The question seeks the square root of a complex number, represented as w = a + bi. To find the square root, one would typically square the complex number and its conjugate to eliminate the imaginary part. However, without the value of 'z', the calculation cannot be completed, and the correct answer cannot be determined from the provided options.
Step-by-step explanation:
The question provided is asking to find the value of w which is the square root of a complex number z. The equation w = a + bi represents a complex number where a is the real part, and b is the imaginary part. To find this square root, one needs to use the property that multiplying a complex number by its conjugate removes the complex parts:
A* A = (a + ib) (a − ib) = a² + b²
However, the second set of equations provided relating to a quadratic with coefficients a, b, and c is not directly relevant to finding the square root of a complex number. Therefore, we will ignore this information. To ascertain which option (A, B, C, or D) represents the correct value of w, we would typically need the value of z to calculate the square root. Without the value of z, we cannot determine which option is the correct value of w. None of the provided options can be matched directly to an answer without additional context or information.