Question

Find the product of each pair of complex conjugates.
(3+8i)(3-8i)=

Answer 1

3*3=9

3 *-8i = -24i

8i *3 =24i

8i*-8i = -64i^2 or i^2 =-1. -64*-1=64

-24i + 24i =0

9+64= 73

Answer 73

Answer 2

The product of each pair of complex conjugates is 73.

Given to us,

(3+8i)(3-8i)

We must know:

a.) $i = \sqrt{(-1)}$

b.) $i^2 = (\sqrt{(-1})^2 = -1$

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

The product of these complex conjugates can be found out in the following ways:

a.) Solving by taking the product

$(3+8i)(3-8i)\\= 9-24i+24i -64i^2\\=9-64(i^2)\\=9-64(-1)\\=9+64\\=73$

b.) Solving using the identity,

$(3+8i)(3-8i)\\=(3)^2-(8i)^2\\= 9 -(-64)\\= 9+64\\=73$

Hence, the product of each pair of complex conjugates is 73.

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