Question

simplify.
$(8i)^2$
write your answer in the form $a + bi$.

Explanation:

Step1: Recall the property of \(i\)

We know that \(i^2 = - 1\).

Step2: Expand \((8i)^2\)

Using the formula \((ab)^2=a^2b^2\), where \(a = 8\) and \(b=i\), we have \((8i)^2=8^2\times i^2\).
Since \(8^2 = 64\) and \(i^2=-1\), then \(8^2\times i^2=64\times(- 1)\).

Step3: Calculate the result

\(64\times(-1)=- 64\), and we can write \(-64\) in the form \(a + bi\) as \(-64+0i\).

Answer:

\(-64 + 0i\) (or simply \(-64\) since the \(bi\) term has a coefficient of \(0\))