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Simplify the expression to a+bi form: sqrt81-sqrt(-8)-sqrt100+sqrt(-98) Answer:

Simplify the expression to a+bi a+b i form:\newline81−−8−100+−98 \sqrt{81}-\sqrt{-8}-\sqrt{100}+\sqrt{-98} \newlineAnswer:

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Full solution

Q. Simplify the expression to a+bi a+b i form:\newline81−−8−100+−98 \sqrt{81}-\sqrt{-8}-\sqrt{100}+\sqrt{-98} \newlineAnswer:
  1. Question Prompt: Question prompt: Simplify the expression to a+bia+bi form: 81−−8−100+−98\sqrt{81}-\sqrt{-8}-\sqrt{100}+\sqrt{-98}.
  2. Given Expression: Given expression:\newline81−−8−100+−98\sqrt{81}-\sqrt{-8}-\sqrt{100}+\sqrt{-98}\newlineExpress the expression using ii for the square roots of negative numbers.\newline81−8i−100+98i\sqrt{81} - \sqrt{8}i - \sqrt{100} + \sqrt{98}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.81−8i−100+98i=9−22i−10+72i\sqrt{81} - \sqrt{8}i - \sqrt{100} + \sqrt{98}i = 9 - 2\sqrt{2}i - 10 + 7\sqrt{2}i
  4. Simplify Square Roots: Combine like terms to simplify the expression further.\newline9−22i−10+72i9 - 2\sqrt{2}i - 10 + 7\sqrt{2}i\newline= (9−10)+(−22i+72i)(9 - 10) + (-2\sqrt{2}i + 7\sqrt{2}i)\newline= −1+52i-1 + 5\sqrt{2}i

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