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Simplify the expression to a+bi form: sqrt49-sqrt(-200)+sqrt81+sqrt(-128) Answer:

Simplify the expression to a+bi a+b i form:\newline49−−200+81+−128 \sqrt{49}-\sqrt{-200}+\sqrt{81}+\sqrt{-128} \newlineAnswer:

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Simplify the expression using imaginary number iright chevron icon

Full solution

Q. Simplify the expression to a+bi a+b i form:\newline49−−200+81+−128 \sqrt{49}-\sqrt{-200}+\sqrt{81}+\sqrt{-128} \newlineAnswer:
  1. Given expression: Given expression:\newline49−−200+81+−128\sqrt{49}-\sqrt{-200}+\sqrt{81}+\sqrt{-128}\newlineExpress the expression using ii for the square roots of negative numbers.\newline49−200i+81+128i\sqrt{49}-\sqrt{200}i+\sqrt{81}+\sqrt{128}i
  2. Express using ii: Simplify the square roots of the positive numbers and express the square roots of the negative numbers in terms of ii.
    49−200i+81+128i\sqrt{49} - \sqrt{200}i + \sqrt{81} + \sqrt{128}i
    = 7−102i+9+82i7 - 10\sqrt{2}i + 9 + 8\sqrt{2}i
  3. Simplify and combine: Combine like terms to get the expression in a+bia+bi form.7−102i+9+82i7 - 10\sqrt{2}i + 9 + 8\sqrt{2}i=(7+9)+(−102i+82i)= (7 + 9) + (-10\sqrt{2}i + 8\sqrt{2}i)=16−22i= 16 - 2\sqrt{2}i

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