To solve the expression \( (2.5 + \sqrt{-36}) - \sqrt{7} \), we first need to simplify each term.
Step 1: Simplify \( \sqrt{-36} \)
Since \(-36\) is negative, we need to express it in terms of imaginary numbers:
\[ \sqrt{-36} = \sqrt{36} \cdot \sqrt{-1} = 6i \]
Step 2: Rewrite the Expression
Now we substitute the simplified form of \( \sqrt{-36} \) into the expression:
\[ (2.5 + 6i) - \sqrt{7} \]
Step 3: Simplifying Further
Since \( \sqrt{7} \) is a real number, we will simply subtract \( \sqrt{7} \) from the real part \( 2.5 \):
\[ 2.5 - \sqrt{7} + 6i \]
Step 4: Final Form
Now we have our expression in the form \( a + bi \). Here, \( a = 2.5 - \sqrt{7} \) and \( b = 6 \).
Thus, the final answer is:
\[ (2.5 - \sqrt{7}) + 6i \]
Summary
The simplified form of the expression \( (2.5 + \sqrt{-36}) - \sqrt{7} \) is
\[ (2.5 - \sqrt{7}) + 6i \]
This is your final answer.