use the imaginary number ( i ) to rewrite the expression below as a complex number. simplify all radicals. (…

use the imaginary number ( i ) to rewrite the expression below as a complex number. simplify all radicals. ( sqrt{-49} )

use the imaginary number ( i ) to rewrite the expression below as a complex number. simplify all radicals. ( sqrt{-49} )

Answer

Explanation:

Step1: Use the property of imaginary numbers

We know that (i = \sqrt{-1}), so (\sqrt{-49}=\sqrt{49\times(-1)}). Using the property (\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}) ((a = 49), (b=-1)), we get (\sqrt{49}\cdot\sqrt{-1}).

Step2: Simplify the radicals

Since (\sqrt{49} = 7) and (\sqrt{-1}=i), then (\sqrt{49}\cdot\sqrt{-1}=7i).

Answer:

(7i)