Question

-2i·(2 + 6i) =
your answer should be a complex number in the form a + bi where a and b are real numbers.

Explanation:

Step1: Use the distributive property (FOIL method)

We need to multiply \(-2i\) with each term inside the parentheses \((2 + 6i)\). So we have \(-2i\times2 + (-2i)\times6i\).

Step2: Simplify each term

First term: \(-2i\times2=-4i\).
Second term: \((-2i)\times6i=-12i^{2}\). But we know that \(i^{2} = - 1\), so \(-12i^{2}=-12\times(-1) = 12\).

Step3: Combine the terms

Now we combine the two simplified terms. We have \(12-4i\) (since we add the real part and the imaginary part together, here the real part is \(12\) and the imaginary part is \(-4i\)).

Answer:

\(12 - 4i\)