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{-38})
Answer
Explanation:
Step1: Rewrite the negative sign inside the square root
$$-\sqrt{-38}=-\sqrt{38\times(- 1)}$$
Step2: Use the property $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$ ($a = 38$, $b=-1$)
$$-\sqrt{38\times(-1)}=-\sqrt{38}\cdot\sqrt{-1}$$
Step3: Recall that $i = \sqrt{-1}$
$$-\sqrt{38}\cdot\sqrt{-1}=-\sqrt{38}i$$
Answer:
$-\sqrt{38}i$