1. **Stating the problem:** We need to find the value of $z$ from the equation: $$\frac{01 = 57 + z^2}{0.25} \times \left(\frac{57 + z^2}{5 + 2.87}\right)^3 \times \left(\frac{}{ }\right)^2 \times \frac{0.0012}{1}$$ Since the problem is a bit unclear, we interpret the expression as: $$\frac{1}{0.25} \times \left(\frac{57 + z^2}{5 + 2.87}\right)^3 \times 0.0012 = 1$$ 2. **Simplify constants:** Calculate the denominator in the fraction: $$5 + 2.87 = 7.87$$ Calculate the first fraction: $$\frac{1}{0.25} = 4$$ 3. **Rewrite the equation:** $$4 \times \left(\frac{57 + z^2}{7.87}\right)^3 \times 0.0012 = 1$$ 4. **Isolate the cubic term:** Divide both sides by $4 \times 0.0012$: $$\left(\frac{57 + z^2}{7.87}\right)^3 = \frac{1}{4 \times 0.0012} = \frac{1}{0.0048} \approx 208.3333$$ 5. **Take the cube root:** $$\frac{57 + z^2}{7.87} = \sqrt[3]{208.3333}$$ Calculate the cube root: $$\sqrt[3]{208.3333} \approx 5.94$$ 6. **Solve for $z^2$:** Multiply both sides by 7.87: $$57 + z^2 = 5.94 \times 7.87 \approx 46.74$$ Subtract 57: $$z^2 = 46.74 - 57 = -10.26$$ 7. **Interpret the result:** Since $z^2$ is negative, there is no real solution for $z$. The value of $z$ would be imaginary: $$z = \pm \sqrt{-10.26} = \pm i \sqrt{10.26} \approx \pm 3.20i$$ **Final answer:** $$z = \pm 3.20i$$