Question

1. 8i - 9i·6i
2. (-4i)³·2i
3. (2i)⁵·(i√6)²

Explanation:

Let's solve problem 14: \((-4i)^3 \cdot 2i\)

Step 1: Simplify \((-4i)^3\)

We use the power of a product rule \((ab)^n = a^n b^n\) and the property \(i^2=-1\), \(i^3 = i^2 \cdot i=-i\).
\[

$$\begin{align*} (-4i)^3&=(-4)^3 \cdot i^3\\ &=-64 \cdot (-i)\\ &= 64i \end{align*}$$

\]

Step 2: Multiply by \(2i\)

Now we multiply the result from step 1 by \(2i\):
\[

$$\begin{align*} 64i \cdot 2i&= 128i^2\\ &= 128 \cdot (-1)\\ &=-128 \end{align*}$$

\]

Answer:

\(-128\)