Question

simplify the expression to a + bi form:
-\sqrt{64}+\sqrt{-16}+\sqrt{81}+\sqrt{-9}
answer attempt 2 out of 2
1 - 7i

Explanation:

Step1: Simplify square - roots of positive numbers

We know that $\sqrt{64} = 8$ and $\sqrt{81}=9$. So, $-\sqrt{64}=-8$ and $\sqrt{81} = 9$.

Step2: Simplify square - roots of negative numbers

Recall that $\sqrt{-x}=i\sqrt{x}$ for $x>0$. So, $\sqrt{-16}=i\sqrt{16}=4i$ and $\sqrt{-9}=i\sqrt{9} = 3i$.

Step3: Combine the real and imaginary parts

\[

$$\begin{align*} -\sqrt{64}+\sqrt{-16}+\sqrt{81}+\sqrt{-9}&=-8 + 4i+9+3i\\ &=(-8 + 9)+(4i+3i)\\ &=1 + 7i \end{align*}$$

\]

Answer:

$1 + 7i$