Evaluate the expression √-16
 and write the result in the form a+bi
.


The expression \( \sqrt{-16} \) involves taking the square root of a negative number, which requires using imaginary numbers. We know that:

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

Thus, \( \sqrt{-16} \) can be rewritten as:

\[
\sqrt{-16} = \sqrt{16 \cdot (-1)} = \sqrt{16} \cdot \sqrt{-1} = 4i
\]

So, the result in the form \( a + bi \) is:

\[
0 + 4i
\]

Would you like further explanation or details?

Here are 5 related questions for practice:

1. What is \( \sqrt{-9} \) in the form \( a + bi \)?
2. How do you simplify \( \sqrt{-25} \)?
3. What is \( \sqrt{-1} \) known as?
4. Convert \( \sqrt{-36} \) to the form \( a + bi \).
5. How do you handle square roots of negative numbers in general?

**Tip:** When dealing with square roots of negative numbers, always factor out \( \sqrt{-1} = i \) first!

Evaluate the expression √-16 and write the result in the form a + bi.

Learn how to evaluate the expression √-16 using imaginary numbers and express the result in the form a + bi. This problem introduces key concepts such as imaginary numbers and complex number operations, suitable for Grades 8-10 students.

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