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 $a{x}^2+bx+c=0$. In this case, $a=1$, $b=1$, and $c=-30$.

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

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

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 $\boxed{{\displaystyle \text{no solution}}}$.