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Simplify the expression to a+bi form: sqrt25+sqrt(-48)+sqrt9+sqrt(-3) Answer:

Simplify the expression to a+bi a+b i form:\newline25+−48+9+−3 \sqrt{25}+\sqrt{-48}+\sqrt{9}+\sqrt{-3} \newlineAnswer:

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Full solution

Q. Simplify the expression to a+bi a+b i form:\newline25+−48+9+−3 \sqrt{25}+\sqrt{-48}+\sqrt{9}+\sqrt{-3} \newlineAnswer:
  1. Question Prompt: Question prompt: Simplify the expression to a+bia+bi form: 25+−48+9+−3\sqrt{25}+\sqrt{-48}+\sqrt{9}+\sqrt{-3}.
  2. Given Expression: Given expression: 25+−48+9+−3\sqrt{25}+\sqrt{-48}+\sqrt{9}+\sqrt{-3} Express the expression using ii for the square roots of negative numbers. 25+−48+9+−3=25+48i+9+3i\sqrt{25}+\sqrt{-48}+\sqrt{9}+\sqrt{-3} = \sqrt{25}+\sqrt{48}i+\sqrt{9}+\sqrt{3}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.25+48i+9+3i=5+43i+3+3i\sqrt{25}+\sqrt{48}i+\sqrt{9}+\sqrt{3}i = 5+4\sqrt{3}i+3+\sqrt{3}i
  4. Simplify Square Roots: Combine like terms to get the expression in a+bia+bi form.5+43i+3+3i5+4\sqrt{3}i+3+\sqrt{3}i=(5+3)+(43i+3i)= (5+3)+(4\sqrt{3}i+\sqrt{3}i)=8+53i= 8+5\sqrt{3}i

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