Rewrite 3+4−45−−−−√ as a complex number in the standard form a+bi.

Answer 1

To rewrite \( 3 + 4 - \sqrt{45} \) as a complex number in standard form \( a + bi \), we first need to simplify the expression.

1. Simplify \( \sqrt{45} \): \[ \sqrt{45} = \sqrt{9 \cdot 5} = \sqrt{9} \cdot \sqrt{5} = 3\sqrt{5} \]

2. Substitute and calculate: \[ 3 + 4 - \sqrt{45} = 3 + 4 - 3\sqrt{5} \] \[ = 7 - 3\sqrt{5} \]

Since there is no imaginary part in this expression, we can express it in standard form \( a + bi \) where \( b = 0 \):

Thus, the complex number in standard form is: \[ 7 - 3\sqrt{5} + 0i \]

So the answer is: \[ 7 - 3\sqrt{5} + 0i \] or simply: \[ 7 - 3\sqrt{5} \]