How to find the solution of a quadratic equation with complex coefficients? I know how to find the solution for a quadratic equation with real coefficients. But if the coefficient changes to complex numbers then what is the change in the solution? Want an example of such equation with solution.
It's no different.  The quadratic formula works regardless of whether the coefficients are real or complex.

Consider the example
$$(3+i)x^2 + (2-i)x + (5+2i) = 0$$

The quadratic formula gives

$$x = \frac{-(2-i) \pm \sqrt{ (2-i)^2-4(3+i)(5+2i) } }{2(3+i)}$$

Simplifying this is kind of a pain, of course.  Under the radical you have to multiply everything out and combine terms.  Eventually you get the radical into the form $\sqrt{M+Ni}$ where $M$ and $N$ are some constants -- in this example, they will be integers.  Then the question is, how do you simplify the square root of a complex number?  (For that, see How do I get the square root of a complex number?).
Let's see if this works.  Kind of unclear how to use these tools, so I just was going to snapshot a quick writeup.