Question

b. \\(\frac{10\pm\sqrt{-16}}{2}\\)
c. \\(\frac{-3\pm\sqrt{-144}}{6}\\)

Explanation:

Part b

Step1: Simplify the square root of a negative number

Recall that $\sqrt{-a} = i\sqrt{a}$ for $a>0$. So, $\sqrt{-16} = i\sqrt{16} = 4i$.
The expression becomes $\frac{10\pm 4i}{2}$.

Step2: Divide each term by 2

Divide 10 and $4i$ by 2: $\frac{10}{2}\pm\frac{4i}{2}=5\pm 2i$.

Step1: Simplify the square root of a negative number

Using the rule $\sqrt{-a} = i\sqrt{a}$ (where $a = 144>0$), we have $\sqrt{-144}=i\sqrt{144} = 12i$.
The expression becomes $\frac{-3\pm 12i}{6}$.

Step2: Divide each term by 6

Divide $-3$ and $12i$ by 6: $\frac{-3}{6}\pm\frac{12i}{6}=-\frac{1}{2}\pm 2i$.

Answer:

$5\pm 2i$

Part c