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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. 8.161 (page 838)

Multiply using the Binomial Squares pattern: ${(- 2 - 5 i)}^{2}$

Short Answer

Expert verified

The answer of the above equation is $- 21 + 20 i$

Step by step solution

01

Given information

We are given a complex number ${(- 2 - 5 i)}^{2}$

02

Use the Product of Binomial Squares Pattern, a+b2=a2+2ab+b2

${(- 2)}^{2} + 2 (- 2) (- 5 i) + {(- 5 i)}^{2}$

03

Simplify

$4 + 20 i + 25 i^{2}$

04

Simplify i2

$4 + 20 i - 25$

05

Simplify the real part

$- 21 + 20 i$

06

Conclusion

The solution of the given equation is $- 21 + 20 i$

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Most popular questions from this chapter

In the following exercises, simplify using absolute value signs as needed. $\sqrt{r^{25}}, \sqrt[5]{p^{8}}, \sqrt[4]{m^{5}}$

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