1. The problem asks to rewrite the expression $7 - \sqrt{-55}$ as a complex number and simplify all radicals. 2. Recall that the imaginary unit $i$ is defined as $i = \sqrt{-1}$. 3. Using this, we can rewrite $\sqrt{-55}$ as $\sqrt{55} \times \sqrt{-1} = \sqrt{55}i$. 4. Substitute back into the expression: $$7 - \sqrt{-55} = 7 - \sqrt{55}i$$ 5. The expression is now in the form $a + bi$ where $a = 7$ and $b = -\sqrt{55}$. 6. Since $\sqrt{55}$ cannot be simplified further (as 55 = 5 \times 11, both prime), this is the simplest form. Final answer: $$7 - \sqrt{55}i$$