Let's break down the expression step by step.

The expression given is: 

\[
(\text{i} \sqrt{7})^2 \times 2\text{i}
\]

### Step 1: Square the first term.
\[
(\text{i} \sqrt{7})^2 = \text{i}^2 \times (\sqrt{7})^2
\]

\(\text{i}^2 = -1\) and \((\sqrt{7})^2 = 7\), so:
\[
(\text{i} \sqrt{7})^2 = -1 \times 7 = -7
\]

### Step 2: Multiply the result by \(2\text{i}\).
Now multiply \(-7\) by \(2\text{i}\):
\[
-7 \times 2\text{i} = -14\text{i}
\]

So the final answer is:

\[
-14\text{i}
\]

Would you like to go into more detail or have any questions? Here are some related questions to explore further:

1. What is the general formula for the square of a complex number?
2. How does multiplying complex numbers differ from multiplying real numbers?
3. Can you explain why \(\text{i}^2 = -1\)?
4. What happens if you multiply two purely imaginary numbers?
5. How do you add or subtract complex numbers?

**Tip:** When dealing with imaginary numbers, remember that \(\text{i}^2 = -1\) is a key property that simplifies many expressions.

Understand how to simplify the expression (i√7)² × 2i with a detailed step-by-step solution. Explore key concepts such as complex numbers, imaginary numbers, and algebraic operations. Ideal for students in Grades 9-11.

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