if i = StartRoot -1 EndRoot, what is the vaule of i^3

Given that \( i = \sqrt{-1} \), which is the imaginary unit, we are tasked with finding \( i^3 \).

We can start by recalling the powers of \( i \):

- \( i^1 = i \)
- \( i^2 = -1 \)
- \( i^3 = i^2 \times i = -1 \times i = -i \)

Thus, \( i^3 = -i \).

Would you like more details on the properties of imaginary numbers?

Here are 5 related questions for further exploration:
1. What is \( i^4 \)?
2. How do the powers of \( i \) repeat in cycles?
3. What is \( i^5 \)?
4. How do imaginary numbers relate to complex numbers?
5. What is the geometric interpretation of multiplying by \( i \)?

**Tip:** Powers of \( i \) repeat in a cycle of four: \( i, -1, -i, 1 \).

if i = StartRoot -1 EndRoot, what is the value of i^3?

Explore how to calculate the value of i^3 where i is the imaginary unit (√-1). Learn key concepts such as the powers of i and how they repeat in cycles. This step-by-step guide is suitable for students in Grades 9-12 learning about imaginary and complex numbers.

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