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Simplify the expression to a+bi form: sqrt144-sqrt(-90)+sqrt1-sqrt(-40) Answer:

Simplify the expression to a+bi a+b i form:\newline144−−90+1−−40 \sqrt{144}-\sqrt{-90}+\sqrt{1}-\sqrt{-40} \newlineAnswer: \newline\

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Q. Simplify the expression to a+bi a+b i form:\newline144−−90+1−−40 \sqrt{144}-\sqrt{-90}+\sqrt{1}-\sqrt{-40} \newlineAnswer: \newline\
  1. Question Prompt: Question prompt: Simplify the expression to a+bia+bi form: 144−−90+1−−40\sqrt{144}-\sqrt{-90}+\sqrt{1}-\sqrt{-40}.
  2. Given Expression: Given expression:\newline144−−90+1−−40\sqrt{144}-\sqrt{-90}+\sqrt{1}-\sqrt{-40}\newlineExpress the expression using ii for the square roots of negative numbers.\newline144−90i+1−40i\sqrt{144} - \sqrt{90}i + \sqrt{1} - \sqrt{40}i
  3. Express Using i: Simplify the square roots of the positive numbers and express the square roots of the negative numbers in terms of i.144−90i+1−40i=12−90i+1−40i\sqrt{144} - \sqrt{90}i + \sqrt{1} - \sqrt{40}i = 12 - \sqrt{90}i + 1 - \sqrt{40}i
  4. Simplify Square Roots: Simplify the square roots that are multiplied by ii.12−90i+1−40i12 - \sqrt{90}i + 1 - \sqrt{40}i=12−9×10i+1−4×10i= 12 - \sqrt{9\times 10}i + 1 - \sqrt{4\times 10}i=12−310i+1−210i= 12 - 3\sqrt{10}i + 1 - 2\sqrt{10}i
  5. Simplify Multiplication: Combine like terms.\newline12−310i+1−210i12 - 3\sqrt{10}i + 1 - 2\sqrt{10}i\newline= (12+1)+(−310i−210i)(12 + 1) + (-3\sqrt{10}i - 2\sqrt{10}i)\newline= 13−510i13 - 5\sqrt{10}i

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