Question

question
simplify the expression to a + bi form:
√121 + √(-27) + √100 + √(-192)

Explanation:

Step1: Simplify square - roots of positive numbers

$\sqrt{121}=11$ and $\sqrt{100} = 10$.

Step2: Simplify square - roots of negative numbers

$\sqrt{-27}=\sqrt{27}\times\sqrt{-1}=3\sqrt{3}i$ and $\sqrt{-192}=\sqrt{192}\times\sqrt{-1}=8\sqrt{3}i$.

Step3: Combine real and imaginary parts

$(11 + 10)+(3\sqrt{3}+8\sqrt{3})i$.
$21 + 11\sqrt{3}i$.

Answer:

$21 + 11\sqrt{3}i$