https://file.aiquickdraw.com/mathbot/file/17264082561658joswdjw.jpg

The expression in the image shows \(\frac{1}{i}\), where \(i\) represents the imaginary unit, defined as \(i = \sqrt{-1}\).

To simplify \(\frac{1}{i}\), we can multiply both the numerator and the denominator by \(i\) to remove the imaginary number from the denominator:

\[
\frac{1}{i} \times \frac{i}{i} = \frac{i}{i^2} = \frac{i}{-1} = -i
\]

Thus, \(\frac{1}{i} = -i\).

Would you like more details on the properties of imaginary numbers or the simplification process? Here are some related questions you might find interesting:

1. What is the meaning of the imaginary unit \(i\)?
2. How do you perform operations with complex numbers?
3. What is the significance of the number \(i^2 = -1\)?
4. How do you divide complex numbers?
5. How do powers of \(i\) behave?

**Tip**: When dealing with imaginary numbers, multiplying by the conjugate is often useful to eliminate imaginary parts in the denominator.

Learn how to simplify the expression 1/i using properties of complex numbers. This problem explores the imaginary unit and demonstrates multiplication by the conjugate to remove imaginary parts in the denominator. Suitable for students in Grades 11-12.

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