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

Simplify the expression to a+bi a+b i form:\newline−121+−54+1−−24 -\sqrt{121}+\sqrt{-54}+\sqrt{1}-\sqrt{-24} \newlineAnswer:

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Full solution

Q. Simplify the expression to a+bi a+b i form:\newline−121+−54+1−−24 -\sqrt{121}+\sqrt{-54}+\sqrt{1}-\sqrt{-24} \newlineAnswer:
  1. Given expression: Given expression:\newline−121+−54+1−−24-\sqrt{121}+\sqrt{-54}+\sqrt{1}-\sqrt{-24}\newlineExpress the expression using ii for the square roots of negative numbers.\newline−121+54i+1−24i-\sqrt{121}+\sqrt{54}i+\sqrt{1}-\sqrt{24}i
  2. Express using i: Simplify the square roots of positive numbers and express the square roots of negative numbers in terms of i.−121+54i+1−24i=−11+54i+1−24i-\sqrt{121}+\sqrt{54}i+\sqrt{1}-\sqrt{24}i = -11+\sqrt{54}i+1-\sqrt{24}i
  3. Simplify square roots: Simplify the square roots that are multiplied by ii.−121+54i+1−24i-\sqrt{121}+\sqrt{54}i+\sqrt{1}-\sqrt{24}i=−11+(9⋅6)i+1−(4⋅6)i= -11+(\sqrt{9}\cdot\sqrt{6})i+1-(\sqrt{4}\cdot\sqrt{6})i=−11+36i+1−26i= -11+3\sqrt{6}i+1-2\sqrt{6}i
  4. Combine like terms: Combine like terms.\newline−11+36i+1−26i-11+3\sqrt{6}i+1-2\sqrt{6}i\newline= (−11+1)+(36i−26i)(-11+1) + (3\sqrt{6}i-2\sqrt{6}i)\newline= −10+6i-10 + \sqrt{6}i

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