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1 vote
Simplify (4+2i)(4-2i)

A. 20
B. 12
C. 16-4i
D. 16+4i

User Mchlstckl
by
9.1k points

2 Answers

4 votes


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

User Palamino
by
7.8k points
3 votes

Answer:

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.

User Sonic Soul
by
8.0k points

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