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

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

Solution

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

Identify the imaginary part by rewriting $\sqrt{-36}$ as $6i$.
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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