To re-express \( 3 - \sqrt{32} \) as a complex number using the imaginary unit \( i = \sqrt{-1} \), we first simplify \( \sqrt{32} \).
\[ \sqrt{32} = \sqrt{16 \times 2} = \sqrt{16} \times \sqrt{2} = 4\sqrt{2} \]
Thus, we can substitute this back into our expression:
\[ 3 - \sqrt{32} = 3 - 4\sqrt{2} \]
Since this expression is purely a real number, we can express it as a complex number:
\[ 3 - 4\sqrt{2} + 0i \]
This means that \( 3 - \sqrt{32} \) can be expressed in standard complex form \( a + bi \) as:
\[ (3 - 4\sqrt{2}) + 0i \]
This is the final expression as a complex number.