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

A

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.