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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. 453 (page 845)

In the following exercises, multiply using the Product of Complex Conjugates Pattern.
$(7 - i) (7 + i)$

Short Answer

Expert verified

The required answer is 50

Step by step solution

01

Step 1. Given Information

The given expression is $(7 - i) (7 + i)$

02

Step 2. Calculation

Simplify the given complex number using the property $(a + b i) (a - b i) = a^{2} + b^{2}$

$(7 - i) (7 + i) = 7^{2} + 1^{1} = 49 + 1 = 50$

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Most popular questions from this chapter

Use the Quotient Property to simplify square roots.

(a) $\sqrt{\frac{32 x^{5} y^{3}}{18 x^{3} y}}$

(b) $\sqrt[3]{\frac{5 x^{6} y^{9}}{40 x^{5} y^{3}}}$

(c) $\sqrt[4]{\frac{5 a^{8} b^{6}}{80 a^{3} b^{2}}}$

In the following exercises, simplify using absolute value signs as needed. $\sqrt{147 m^{7} n^{11}}, \sqrt[3]{48 x^{6} y^{7}}, \sqrt[4]{32 x^{5} y^{4}}$

Explain what is meant by the $n^{t h}$ root of a number.

In the following exercises, solve.

$\sqrt{4 m + 2} + 2 = 6$

Why is there no real number equal to $\sqrt{- 64}$ ?

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