Question

4i(5 - 3i)

Explanation:

Step1: Use the distributive property (multiplication over subtraction)

We know that for any complex numbers \(a\), \(b\), and \(c\), \(a(b - c)=ab - ac\). Here \(a = 4i\), \(b = 5\), and \(c = 3i\). So we have:
\(4i\times5-4i\times3i\)

Step2: Simplify each term

First term: \(4i\times5 = 20i\)
Second term: Recall that \(i^2=- 1\), so \(4i\times3i=12i^{2}=12\times(-1)=- 12\)
Now we have \(20i-(-12)=20i + 12\)
We can rewrite it in the standard form of a complex number \(a+bi\) as \(12 + 20i\)

Answer:

\(12 + 20i\)