Question

simplify.
(4 + 2i)(6 - 3i)
? + i

Explanation:

Step1: Apply the distributive property (FOIL method)

Multiply the First terms: \(4\times6 = 24\)
Multiply the Outer terms: \(4\times(-3i)= -12i\)
Multiply the Inner terms: \(2i\times6 = 12i\)
Multiply the Last terms: \(2i\times(-3i)= -6i^{2}\)
So, \((4 + 2i)(6 - 3i)=24-12i + 12i-6i^{2}\)

Step2: Simplify using \(i^{2}=-1\)

Combine like terms for the imaginary parts: \(-12i + 12i = 0\)
Substitute \(i^{2}=-1\) into \(-6i^{2}\): \(-6\times(-1)=6\)
Now, add the real parts: \(24 + 6=30\)
And the imaginary part is \(0\) (since \(-12i + 12i = 0\))

Answer:

\(30 + 0i\)