Simplify the expression to a+bi form: -sqrt121+sqrt(-54)+sqrt1-sqrt(-24) Answer:

Given expression: Given expression: -sqrt(121)+sqrt(-54)+sqrt(1)-sqrt(-24) Express the expression using i for the square roots of negative numbers. -sqrt(121)+sqrt(-54)+sqrt(1)-sqrt(-24) = -sqrt(121)+sqrt(54)i+sqrt(1)-sqrt(24)iExpress using i: Simplify the square roots of positive numbers and express the square roots of negative numbers in terms of i. -sqrt(121)+sqrt(54)i+sqrt(1)-sqrt(24)i = -11+sqrt(54)i+1-sqrt(24)iSimplify square roots: Simplify the square roots that are multiplied by i. -sqrt(121)+sqrt(54)i+sqrt(1)-sqrt(24)i = -11+(sqrt(9)*sqrt(6))i+1-(sqrt(4)*sqrt(6))i = -11+3sqrt(6)i+1-2sqrt(6)iCombine like terms: Combine like terms. -11+3sqrt(6)i+1-2sqrt(6)i = (-11+1) + (3sqrt(6)i-2sqrt(6)i) = -10 + sqrt(6)i

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Algebra 2

Simplify the expression using imaginary number i

Full solution

Q. Simplify the expression to

a+b i

form:

\newline

-\sqrt{121}+\sqrt{-54}+\sqrt{1}-\sqrt{-24}

\newline

Answer:

Given expression: Given expression: $\newline$ $-\sqrt{121}+\sqrt{-54}+\sqrt{1}-\sqrt{-24}$ $\newline$ Express the expression using $i$ for the square roots of negative numbers. $\newline$ $-\sqrt{121}+\sqrt{54}i+\sqrt{1}-\sqrt{24}i$
Express using i: Simplify the square roots of positive numbers and express the square roots of negative numbers in terms of i. $-\sqrt{121}+\sqrt{54}i+\sqrt{1}-\sqrt{24}i = -11+\sqrt{54}i+1-\sqrt{24}i$
Simplify square roots: Simplify the square roots that are multiplied by $i$ . $-\sqrt{121}+\sqrt{54}i+\sqrt{1}-\sqrt{24}i$ $= -11+(\sqrt{9}\cdot\sqrt{6})i+1-(\sqrt{4}\cdot\sqrt{6})i$ $= -11+3\sqrt{6}i+1-2\sqrt{6}i$
Combine like terms: Combine like terms. $\newline$ $-11+3\sqrt{6}i+1-2\sqrt{6}i$ $\newline$ = $(-11+1) + (3\sqrt{6}i-2\sqrt{6}i)$ $\newline$ = $-10 + \sqrt{6}i$