To rewrite \( 3 + 4 - \sqrt{45} \) in the standard form \( a + bi \), we start by simplifying the expression.
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First, simplify \( \sqrt{45} \): \[ \sqrt{45} = \sqrt{9 \cdot 5} = \sqrt{9} \cdot \sqrt{5} = 3\sqrt{5} \]
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Now substitute \( \sqrt{45} \) back into the expression: \[ 3 + 4 - \sqrt{45} = 3 + 4 - 3\sqrt{5} \]
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Combine the constant terms: \[ 3 + 4 = 7 \] Therefore, the expression simplifies to: \[ 7 - 3\sqrt{5} \]
Since there are no imaginary components in this expression, we can express it in the standard complex number form \( a + bi \):
- Here, \( a = 7 - 3\sqrt{5} \) and \( b = 0 \).
Thus, the final result is: \[ 7 - 3\sqrt{5} + 0i \]
In standard form, this is: \[ (7 - 3\sqrt{5}) + 0i \]