It looks like there was a small typo in your expression. I'll assume you meant to calculate \(\imaginaryI^3\).

The imaginary unit \(\imaginaryI\) is defined as:

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

To find \(\imaginaryI^3\):

\[
\imaginaryI^3 = \imaginaryI \times \imaginaryI \times \imaginaryI
\]

Since \(\imaginaryI \times \imaginaryI = \imaginaryI^2 = -1\), we can further calculate:

\[
\imaginaryI^3 = \imaginaryI^2 \times \imaginaryI = -1 \times \imaginaryI = -\imaginaryI
\]

Therefore, 

\[
\imaginaryI^3 = -\imaginaryI
\]

Would you like more details or have any questions about this? Here are some related questions to consider:

1. What is \(\imaginaryI^4\)?
2. How do powers of \(\imaginaryI\) repeat in a cycle?
3. What are complex numbers, and how do they relate to \(\imaginaryI\)?
4. How do you multiply and divide complex numbers?
5. What is the geometric interpretation of multiplying by \(\imaginaryI\)?

**Tip:** Powers of \(\imaginaryI\) cycle every four terms: \(\imaginaryI, -1, -\imaginaryI, 1\).

Explore the calculation of \(\imaginaryI^3\) in complex numbers, where \(\imaginaryI\) is the imaginary unit defined as the square root of negative one. Learn how powers of \(\imaginaryI\) cycle every four terms and its relevance in complex number theory.

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