Express the radical using the imaginary unit, i. Express your answer in simplified form. +-sqrt(-100)=+-◻

Recognizing the imaginary unit: First, we recognize that the square root of a negative number involves the imaginary unit i, where i^2 = -1. We can rewrite the expression ±sqrt(-100) by factoring out the negative as the square root of -1 times the square root of 100.Factoring out the negative: Next, we know that sqrt(-1) is equal to i, and sqrt(100) is equal to 10. So we can express ±sqrt(-100) as ±i * sqrt(100).Simplifying the expression: Now, we simplify the expression by multiplying i with the square root of 100, which is 10. This gives us ±i * 10, which can be written as ±10i.Final simplified complex number form: Finally, we have the expression in its simplest form, which is ±10i. This is the simplified complex number form of the original expression ±sqrt(-100).

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Express the radical using the imaginary unit,
i.
Express your answer in simplified form.

+-sqrt(-100)=+-◻

Express the radical using the imaginary unit, $i$ . $\newline$ Express your answer in simplified form. $\newline$ $\pm \sqrt{-100}= \pm \square$

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Algebra 2

Introduction to complex numbers

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Q. Express the radical using the imaginary unit,

i

\newline

Express your answer in simplified form.

\newline

\pm \sqrt{-100}= \pm \square

Recognizing the imaginary unit: First, we recognize that the square root of a negative number involves the imaginary unit $i$ , where $i^2 = -1$ . We can rewrite the expression $\pm\sqrt{-100}$ by factoring out the negative as the square root of $-1$ times the square root of $100$ .
Factoring out the negative: Next, we know that $\sqrt{-1}$ is equal to $i$ , and $\sqrt{100}$ is equal to $10$ . So we can express $\pm\sqrt{-100}$ as $\pm i \times \sqrt{100}$ .
Simplifying the expression: Now, we simplify the expression by multiplying $i$ with the square root of $100$ , which is $10$ . This gives us $\pm i \times 10$ , which can be written as $\pm 10i$ .
Final simplified complex number form: Finally, we have the expression in its simplest form, which is $\pm 10i$ . This is the simplified complex number form of the original expression $\pm\sqrt{-100}$ .