Write the number in standard form.
StartFraction 4 minus StartRoot negative 128 EndRoot Over 2 EndFraction


Let's simplify the given expression step by step.

We have:

\[
\frac{4 - \sqrt{-128}}{2}
\]

### Step 1: Simplify the square root of a negative number

\[
\sqrt{-128} = \sqrt{-1 \times 128} = \sqrt{-1} \times \sqrt{128} = i \times \sqrt{128}
\]

Since \( \sqrt{128} = \sqrt{64 \times 2} = 8\sqrt{2} \), we get:

\[
\sqrt{-128} = 8i\sqrt{2}
\]

### Step 2: Substitute this into the original expression

\[
\frac{4 - 8i\sqrt{2}}{2}
\]

### Step 3: Simplify the fraction

Now, divide both terms in the numerator by 2:

\[
= \frac{4}{2} - \frac{8i\sqrt{2}}{2}
\]

\[
= 2 - 4i\sqrt{2}
\]

### Final Answer:

The number in standard form is:

\[
2 - 4i\sqrt{2}
\]

Would you like any further clarification or details? Here are 5 related questions you could explore:

1. How do you simplify square roots involving negative numbers?
2. What are the properties of imaginary numbers?
3. How do you convert a complex number into polar form?
4. How do you simplify radical expressions?
5. How do operations with imaginary numbers differ from real numbers?

**Tip:** When dealing with square roots of negative numbers, always factor out \(i = \sqrt{-1}\) to separate real and imaginary parts.

Write the number in standard form. StartFraction 4 minus StartRoot negative 128 EndRoot Over 2 EndFraction

Learn how to simplify the expression involving complex numbers: (4 - sqrt(-128)) / 2. This problem explores the use of imaginary numbers, radical expressions, and properties of square roots. Ideal for students in Grades 9-12.

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