To solve the equation \(- (x - 3)^2 - 3 = 7\), we start by isolating the quadratic expression. First, add 3 to both sides of the equation:
\[ -(x - 3)^2 = 10 \]
Next, multiply both sides by -1:
\[ (x - 3)^2 = -10 \]
Now we take the square root of both sides. Remember that the square root of a negative number will involve imaginary numbers:
\[ x - 3 = \pm \sqrt{-10} \]
This can be rewritten using the imaginary unit \(i\):
\[ x - 3 = \pm \sqrt{10} i \]
Now, we can solve for \(x\) by adding 3 to both sides:
\[ x = 3 \pm \sqrt{10} i \]
Thus, the solutions to the equation are:
\[ x = 3 + \sqrt{10} i \quad \text{and} \quad x = 3 - \sqrt{10} i \]
These can be expressed in the standard form of a complex number \(a + bi\):
- \(x = 3 + \sqrt{10} i\)
- \(x = 3 - \sqrt{10} i\)
Hence, the solutions in standard form are:
\[ \boxed{3 \pm \sqrt{10} i} \]