a) $i^{2}+i-30=0$

Step 1 ：Given the equation \(i^{2}+i-30=0\). This is a quadratic equation in the complex number \(i\).

Step 2 ：We can solve it using the quadratic formula \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\), where \(a\), \(b\), and \(c\) are the coefficients of the quadratic equation \(ax^2 + bx + c = 0\). In this case, \(a = 1\), \(b = 1\), and \(c = -30\).

Step 3 ：Calculate the discriminant \(D = b^2 - 4ac = (1)^2 - 4*1*(-30) = 121\).

Step 4 ：Find the solutions using the quadratic formula: \(sol1 = \frac{-b - \sqrt{D}}{2a} = \frac{-1 - \sqrt{121}}{2*1} = -6\) and \(sol2 = \frac{-b + \sqrt{D}}{2a} = \frac{-1 + \sqrt{121}}{2*1} = 5\).

Step 5 ：The solutions to the equation are \(i = -6\) and \(i = 5\). However, these solutions are not valid because \(i\) is a complex unit and its value is \(\sqrt{-1}\).

Step 6 ：Final Answer: The equation \(i^{2}+i-30=0\) has \(\boxed{\text{no solution}}\).