To simplify the expression \( 75 - \sqrt{-45} \), we first need to simplify \( \sqrt{-45} \).
We know that:
\[ \sqrt{-45} = \sqrt{45} \cdot \sqrt{-1} = \sqrt{45} i \]
Next, we can simplify \( \sqrt{45} \):
\[ \sqrt{45} = \sqrt{9 \cdot 5} = \sqrt{9} \cdot \sqrt{5} = 3\sqrt{5} \]
So,
\[ \sqrt{-45} = 3\sqrt{5} i \]
Now, we can substitute this back into the original expression:
\[ 75 - \sqrt{-45} = 75 - 3\sqrt{5} i \]
The difference is:
\[ 75 - 3\sqrt{5} i \]
This is the final answer in the form of a complex number, where the real part is 75 and the imaginary part is \(-3\sqrt{5}\). Thus, the expression \( 75 - \sqrt{-45} \) simplifies to:
\[ 75 - 3\sqrt{5} i \]
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