We are asked to solve two complex number problems. First, calculate $(7 - \sqrt{-1}) - \sqrt{-81}$. Second, calculate $2(3-7i) - i(-4+5i)$.

1. Problem Description

We are asked to solve two complex number problems.

First, calculate $(7 - \sqrt{-1}) - \sqrt{-81}$.

Second, calculate $2(3-7i) - i(-4+5i)$.

2. Solution Steps

Problem 23:

We know that $\sqrt{-1} = i$. Also, $\sqrt{-81} = \sqrt{81 \cdot (-1)} = \sqrt{81} \cdot \sqrt{-1} = 9i$. Therefore,

$(7 - \sqrt{-1}) - \sqrt{-81} = (7 - i) - 9i = 7 - i - 9i = 7 - 10i$.

Problem 25:

We have $2(3-7i) - i(-4+5i)$.

First distribute the terms:

$2(3-7i) = 6 - 14i$

$i(-4+5i) = -4i + 5i^2 = -4i + 5(-1) = -5 - 4i$

So we have $2(3-7i) - i(-4+5i) = (6 - 14i) - (-5 - 4i) = 6 - 14i + 5 + 4i = 11 - 10i$.

3. Final Answer

Problem 23:

$7 - 10i$

Problem 25:

$11 - 10i$