The given expression in the image is:

$1 + 5i + 2i^2 - 23i^3$

Step-by-Step Solution:

1. Simplify Powers of $i$:

   • We know that $i$ is the imaginary unit where $i^2 = -1$.
   • $i^3 = i^2 \cdot i = -1 \cdot i = -i$.

2. Substitute these values:

   • $i^2 = -1$,
   • $i^3 = -i$.

Thus, the expression becomes: $1 + 5i + 2(-1) - 23(-i)$

This simplifies to: $1 + 5i - 2 + 23i$

3. Combine real and imaginary parts:
   • Real part: $1 - 2 = -1$,
   • Imaginary part: $5i + 23i = 28i$.

Therefore, the simplified expression is: $-1 + 28i$

This is the final form of the expression in standard form $a + bi$, where $a = -1$ and $b = 28$.

Would you like more details on how powers of $i$ work, or any other part of the process?

Here are 5 related questions:

1. What are the higher powers of $i$ beyond $i^3$?
2. How do we graph complex numbers like $-1 + 28i$ on the complex plane?
3. What are some applications of imaginary numbers in real-life scenarios?
4. How would you add or subtract two complex numbers?
5. Can you multiply or divide two complex numbers, and what does the result represent?

Tip: Always simplify powers of $i$ in steps when working with complex numbers to avoid errors.