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{-36}
Answer
Explanation:
Step1: Rewrite the square root of a negative number
We know that $\sqrt{-a}=\sqrt{a}\times i$ for $a>0$. So, $\sqrt{-36}=\sqrt{36}\times i$.
Step2: Simplify the radical
Since $\sqrt{36} = 6$, then $\sqrt{-36}=6i$.
Step3: Apply the negative sign
The original expression is $-\sqrt{-36}$, substituting the value from Step 2, we get $-(6i)=-6i$.
Answer:
$-6i$