Questions: Write the number as the product of a real number and i. -√(-50) (Simplify your answer. Type your answer in the form a + bi. Type an exact radicals as needed.)

Write the number as the product of a real number and i. -√(-50) (Simplify your answer. Type your answer in the form a + bi. Type an exact radicals as needed.)

Transcript text: Write the number as the product of a real number and $i$. \[ -\sqrt{-50} \] (Simplify your answer. Type your answer in the form a + bi. Type an exact radicals as needed.)

Solution

Solution Steps

Solution

Step 1: Recognize the square root of a negative number in terms of $i$

Given the expression $\sqrt{-n}$, we recognize that it represents the square root of a negative number. In mathematics, the square root of a negative number can be expressed using the imaginary unit $i$, where $i = \sqrt{-1}$.

Step 2: Rewrite the expression

We can rewrite $\sqrt{-n}$ as $\sqrt{n} \cdot \sqrt{-1}$.

Step 3: Simplify the expression

Simplifying $\sqrt{-1}$ to $i$, the expression becomes $\sqrt{n} \cdot i = 7.07i$.