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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. 438 (page 844)

In the following exercise, multiply using the Product of Binomial Squares Pattern.
${(- 1 + 5 i)}^{2}$

Short Answer

Expert verified

The value of the expression ${(- 1 + 5 i)}^{2}$ is equal to $- 24 - 10 i$ .

Step by step solution

01

Step 1. Given information.

An expression is ${(- 1 + 5 i)}^{2}$ .

02

Step 2. Multiply the expression.

Use the formula: ${(a + b)}^{2} = a^{2} + b^{2} + 2 a b$

So,

{(- 1 + 5 i)}^{2} = {(- 1)}^{2} + 2 (- 1) (5 i) + {(5 i)}^{2} = 1 - 10 i + 25 i^{2} = 1 - 10 i - 25 = - 24 - 10 i

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Most popular questions from this chapter

In the following exercises, use the Product Property to simplify radical expressions $\sqrt{147}$

Use the Quotient Property to simplify square roots.

(a) $\sqrt{\frac{50 r^{5} s^{2}}{128 r^{2} s^{6}}}$

(b) $\sqrt[3]{\frac{24 m^{9} n^{7}}{375 m^{4} n}}$

(c) $\sqrt[4]{\frac{81 m^{2} n^{8}}{256 m n^{2}}}$

In the following exercises, solve.

$\sqrt{3 y - 4} = - 2$

What is the difference between $9^{2}$ and $\sqrt{9}$ ?

In the following exercises, write with a rational exponent.

$(a) \sqrt[5]{u^{2}} (b) (\sqrt[3]{6 x})^{5} (c) \sqrt[4]{{(\frac{18 a}{5 b})}^{7}}$

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