Questions: Write the following complex number in standard form: 6-√(-36)

Write the following complex number in standard form: 6-√(-36)
Transcript text: Write the following complex number in standard form: $6-\sqrt{-36}$
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Solution

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Solution Steps

To write the given expression as a complex number, we need to recognize that the square root of a negative number involves the imaginary unit \(i\), where \(i = \sqrt{-1}\). Specifically, \(\sqrt{-36}\) can be rewritten using \(i\).

Solution Approach
  1. Identify the imaginary part by rewriting \(\sqrt{-36}\) as \(6i\).
  2. Combine the real part and the imaginary part to form the complex number.
Step 1: Identify the Imaginary Part

To rewrite \(\sqrt{-36}\), we recognize that \(\sqrt{-1} = i\). Therefore: \[ \sqrt{-36} = \sqrt{36 \cdot (-1)} = \sqrt{36} \cdot \sqrt{-1} = 6i \]

Step 2: Combine Real and Imaginary Parts

The given expression is \(6 - \sqrt{-36}\). Substituting the imaginary part, we get: \[ 6 - 6i \]

Final Answer

The complex number is: \[ \boxed{6 - 6i} \]

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