Question

Simplify (4+2i)(4-2i) A. 20 B. 12 C. 16-4i D. 16+4i

Answer 1

$(a+b)(a-b)=a^2-b^2\\\\(4+2i)(4-2i)=4^2-(2i)^2=\boxed{16-4i^2}$

Answer 2

Answer:

A

Step-by-step explanation:

We want to simplify the expression:

$(4 + 2i)(4- 2i)$

Notice that this is the difference of two squares. That is:

$(a +b)(a-b) = a^2 - b^2$

We can let a = 4 and b = 2i. Hence:

$(4+2i)(4-2i) = (4)^2 - (2i)^2$

Simplify:

$= (16) - (4i^2) \\ \\ = 16 - (-4) \\ \\ = 20$

(Note that i² = -1.)

In conclusion, our answer is A.