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

Question Prompt: Question prompt: Simplify the expression to a+bi form: sqrt144-sqrt(-90)+sqrt1-sqrt(-40).Given Expression: Given expression: sqrt144-sqrt(-90)+sqrt1-sqrt(-40) Express the expression using i for the square roots of negative numbers. sqrt144-sqrt(-90)+sqrt1-sqrt(-40) = sqrt144 - sqrt90i + sqrt1 - sqrt40iExpress Using i: Simplify the square roots of the positive numbers and express the square roots of the negative numbers in terms of i. sqrt144 - sqrt90i + sqrt1 - sqrt40i = 12 - sqrt(90)i + 1 - sqrt(40)iSimplify Square Roots: Simplify the square roots that are multiplied by i. 12 - sqrt(90)i + 1 - sqrt(40)i = 12 - sqrt(9*10)i + 1 - sqrt(4*10)i = 12 - 3sqrt(10)i + 1 - 2sqrt(10)iSimplify Multiplication: Combine like terms. 12 - 3sqrt(10)i + 1 - 2sqrt(10)i = (12 + 1) + (-3sqrt(10)i - 2sqrt(10)i) = 13 - 5sqrt(10)i

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Algebra 2

Simplify the expression using imaginary number i

Full solution

Q. Simplify the expression to

a+b i

form:

\newline

\sqrt{144}-\sqrt{-90}+\sqrt{1}-\sqrt{-40}

\newline

Answer:

\newline\

Question Prompt: Question prompt: Simplify the expression to $a+bi$ form: $\sqrt{144}-\sqrt{-90}+\sqrt{1}-\sqrt{-40}$ .
Given Expression: Given expression: $\newline$ $\sqrt{144}-\sqrt{-90}+\sqrt{1}-\sqrt{-40}$ $\newline$ Express the expression using $i$ for the square roots of negative numbers. $\newline$ $\sqrt{144} - \sqrt{90}i + \sqrt{1} - \sqrt{40}i$
Express Using i: Simplify the square roots of the positive numbers and express the square roots of the negative numbers in terms of i. $\sqrt{144} - \sqrt{90}i + \sqrt{1} - \sqrt{40}i = 12 - \sqrt{90}i + 1 - \sqrt{40}i$
Simplify Square Roots: Simplify the square roots that are multiplied by $i$ . $12 - \sqrt{90}i + 1 - \sqrt{40}i$ $= 12 - \sqrt{9\times 10}i + 1 - \sqrt{4\times 10}i$ $= 12 - 3\sqrt{10}i + 1 - 2\sqrt{10}i$
Simplify Multiplication: Combine like terms. $\newline$ $12 - 3\sqrt{10}i + 1 - 2\sqrt{10}i$ $\newline$ = $(12 + 1) + (-3\sqrt{10}i - 2\sqrt{10}i)$ $\newline$ = $13 - 5\sqrt{10}i$