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Simplify the expression to a+bi form: -sqrt144+sqrt(-80)+sqrt1+sqrt(-5) Answer:

Simplify the expression to a+bi a+b i form:\newline−144+−80+1+−5 -\sqrt{144}+\sqrt{-80}+\sqrt{1}+\sqrt{-5} \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:\newline−144+−80+1+−5 -\sqrt{144}+\sqrt{-80}+\sqrt{1}+\sqrt{-5} \newlineAnswer:
  1. Given expression: Given expression:\newline−144+−80+1+−5-\sqrt{144}+\sqrt{-80}+\sqrt{1}+\sqrt{-5}\newlineExpress the expression using ii for the square roots of negative numbers.\newline−144+80i+1+5i-\sqrt{144}+\sqrt{80}i+\sqrt{1}+\sqrt{5}i
  2. Express using i: Simplify the square roots of the positive numbers and express the square roots of negative numbers in terms of i.\newline−144+80i+1+5i-\sqrt{144}+\sqrt{80}i+\sqrt{1}+\sqrt{5}i\newline=−12+16⋅5i+1+5i= -12+\sqrt{16\cdot 5}i+1+\sqrt{5}i\newline=−12+45i+1+5i= -12+4\sqrt{5}i+1+\sqrt{5}i
  3. Simplify square roots: Combine like terms.\newline−12+45i+1+5i-12+4\sqrt{5}i+1+\sqrt{5}i\newline=(−12+1)+(45i+5i)= (-12+1)+(4\sqrt{5}i+\sqrt{5}i)\newline=−11+55i= -11+5\sqrt{5}i

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