Question

simplify.
-6i cdot 3i
write your answer in the form a + bi.

Explanation:

Step1: Recall the property of \(i\)

We know that \(i^2 = - 1\). Now we need to calculate \(-6i\cdot3i\).
First, multiply the coefficients and the imaginary units separately: \(-6i\cdot3i=(-6\times3)\times(i\times i)\)

Step2: Calculate the product

Calculate \(-6\times3=-18\) and \(i\times i = i^{2}\). So we have \(-18\times i^{2}\).
Since \(i^{2}=-1\), substitute \(i^{2}\) with \(-1\): \(-18\times(-1)=18\)
In the form \(a + bi\), \(a = 18\) and \(b = 0\), so the result is \(18+0i\) or simply \(18\).

Answer:

\(18 + 0i\) (or \(18\))