To simplify the expression $-8i^3 + i^2$, we'll use the properties of the imaginary unit $i$, where:

$i^2 = -1 \quad \text{and} \quad i^3 = -i$

Step-by-step simplification:

1. Simplify $i^2$: $i^2 = -1$

2. Simplify $i^3$: $i^3 = -i$

3. Substitute these values back into the expression: $-8i^3 + i^2 = -8(-i) + (-1)$

4. Simplify: $-8(-i) + (-1) = 8i - 1$

Final Answer:

The simplified expression in standard form is: $8i - 1$

The standard form of a complex number is $a + bi$, where $a$ is the real part and $b$ is the imaginary part. So the final answer is:

$-1 + 8i$

Would you like more details on any part of this solution?

Here are five related questions to explore:

1. What are the higher powers of $i$ (e.g., $i^4, i^5$)?
2. How do you multiply two complex numbers?
3. How do you find the magnitude of a complex number?
4. What is the conjugate of a complex number?
5. How do you add or subtract complex numbers?

Tip: Memorizing the cycle of powers of $i$ helps simplify complex number expressions easily!