b) $3 i^{2}-8 i-7=0$

Step 1 ：We are given the quadratic equation in complex numbers: \(3 i^{2}-8 i-7=0\).

Step 2 ：The general form of a quadratic equation is \(ax^{2} + bx + c = 0\).

Step 3 ：The solutions to this equation can be found using the quadratic formula \(x = \frac{-b \pm \sqrt{b^{2}-4ac}}{2a}\).

Step 4 ：In this case, \(a = 3i\), \(b = -8i\), and \(c = -7\).

Step 5 ：We substitute these values into the quadratic formula to find the solutions.

Step 6 ：First, we calculate the discriminant \(D = b^{2}-4ac = (4.560867804461815+9.208773812499487j)\).

Step 7 ：Then, we find the first solution \(sol1 = \frac{-b + \sqrt{D}}{2a} = (-0.20146230208324786+0.7601446340769692j)\).

Step 8 ：Next, we find the second solution \(sol2 = \frac{-b - \sqrt{D}}{2a} = (2.8681289687499145-0.7601446340769692j)\).

Step 9 ：Finally, we simplify the solutions to get the final answer.

Step 10 ：The solutions to the equation \(3 i^{2}-8 i-7=0\) are \(\boxed{-0.201 + 0.760i}\) and \(\boxed{2.868 - 0.760i}\).