23. $$ \left(2+i^{4}\right)\left(-3-i^{3}\right) $$

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To simplify the expression $$ \left(2+i^{4}\right)\left(-3-i^{3}\right) $$, let's break it down step by step.

1. **Evaluate $$ i^3 $$ and $$ i^4 $$:**
   
   Recall that $$ i $$ is the imaginary unit, where $$ i^2 = -1 $$.
   
   - $$ i^3 = i^2 \cdot i = (-1) \cdot i = -i $$
   - $$ i^4 = (i^2)^2 = (-1)^2 = 1 $$

2. **Substitute the values back into the expression:**

$$
   \left(2 + i^4\right)\left(-3 - i^3\right) = \left(2 + 1\right)\left(-3 - (-i)\right) = 3 \left(-3 + i\right)
   $$

3. **Multiply out the terms:**

$$
   3 \left(-3 + i\right) = 3 \cdot (-3) + 3 \cdot i = -9 + 3i
   $$

So, the simplified form of the expression is:

$$
-9 + 3i
$$

**Answer:** $$-9 + 3i$$
The simplified form of the expression is $$-9 + 3i$$.

23. \( \left(2+i^{4}\right)\left(-3-i^{3}\right) \)

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