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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 8: Q. 573. (page 856)

In the following exercises, multiply using the Product of Binomial Squares Pattern.

Short Answer

Expert verified

Square of the given complex number is ${(- 2 - 3 i)}^{2}$ .

Step by step solution

01

Step 1. Given information.

The given complex number is ${(- 2 - 3 i)}^{2}$ .

02

Step 2. Multiply the complex number.

According to the Binomial Squares Pattern,

${(a + b)}^{2} = a^{2} + 2 a b + b^{2}$

Use this concept, we will get

${(- 2 - 3 i)}^{2} = {(- 2)}^{2} + 2 路 (- 2) 路 (- 3 i) + {(- 3 i)}^{2} = 4 + 12 i + 9 i^{2}$

We know that,

$i^{2} = - 1$

then

${(- 2 - 3 i)}^{2} = 4 + 12 i + 9 (- 1) = 4 + 12 i - 9 = - 5 + 12 i$

03

Step 3. Conclusion.

Therefore, the multiplication of the given complex number is $- 5 + 12 i$ .

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Most popular questions from this chapter

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