Question

use the imaginary number i to rewrite the expression simplify all radicals. \\(sqrt{-100}\\)

Explanation:

Step1: Recall the definition of imaginary unit

The imaginary unit \( i \) is defined as \( i = \sqrt{-1} \). So we can rewrite \( \sqrt{-100} \) as \( \sqrt{-1 \times 100} \).

Step2: Use the property of square roots

Using the property \( \sqrt{ab}=\sqrt{a}\times\sqrt{b} \) (for \( a\geq0, b\geq0 \), and here we extend it for complex numbers), we have \( \sqrt{-1 \times 100}=\sqrt{-1}\times\sqrt{100} \).

Step3: Substitute \( i \) and simplify \( \sqrt{100} \)

Since \( \sqrt{-1}=i \) and \( \sqrt{100} = 10 \), we get \( i\times10 = 10i \).

Answer:

\( 10i \)