Question

which expression is equivalent to ((4\text{i})^{2})?
a. (-16)
b. (16)
c. (-16\text{i})
d. (16\text{i})

Explanation:

Step1: Recall the power of a product rule

The power of a product rule states that \((ab)^n = a^n b^n\). So for \((4i)^2\), we can apply this rule as \((4i)^2 = 4^2\times i^2\).

Step2: Calculate \(4^2\) and recall the definition of \(i\)

First, calculate \(4^2 = 16\). Then, recall that in complex numbers, \(i\) is the imaginary unit where \(i = \sqrt{-1}\), so \(i^2 = (\sqrt{-1})^2=-1\).

Step3: Multiply the results

Now, multiply the two results together: \(16\times(-1)= - 16\).

Answer:

A. \(-16\)