Questions: Express -1+√(-100) as a complex number, expressed in terms of i, and simplified. -1+√(-100)=

Express -1+√(-100) as a complex number, expressed in terms of i, and simplified. -1+√(-100)=
Transcript text: Express $-1+\sqrt{-100}$ as a complex number, expressed in terms of $i$, and simplified. \[ -1+\sqrt{-100}= \] $\square$ Question Help: Video Submit Question
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Solution

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Solution Steps

Step 1: Recognize the square root of a negative number as a complex number

Given a positive real number \(n\), we need to express \(\sqrt{-n}\) in terms of \(i\), where \(i\) is the imaginary unit defined by \(i^2 = -1\).

Step 2: Express \(\sqrt{-n}\) as \(\sqrt{n} \cdot i\)

For the given positive real number \(n = 100\), we express \(\sqrt{-n}\) as \(\sqrt{100} \cdot i\).

Step 3: Simplify the expression

Simplifying the expression, we get \(0 + 10.0i\).

Final Answer:

The expression \(\sqrt{-100}\) in terms of \(i\) is \(0 + 10.0i\).

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