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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 8: Q. 571 (page 856)

Multiply Complex Numbers
$\sqrt{- 4} . \sqrt{- 16}$

Short Answer

Expert verified

The Solution is $- 8$

Step by step solution

01

Given Information

$\sqrt{- 4} . \sqrt{- 16}$ The Given Equation is

02

Simplify the terms to complex numbers

$\sqrt{- 4} & \sqrt{- 16}$

Simplifying $\sqrt{- 4}$

$i . \sqrt{4}$

$2 i$

Simplifying $\sqrt{- 16}$

$i . \sqrt{16}$

$4 i$

03

Multiplying The terms

$= (2 i) (4 i) = 8 i^{2} = - 8$

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Most popular questions from this chapter

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

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

Use the Quotient Property to simplify square roots.

(a) $\frac{\sqrt{72 n^{11}}}{\sqrt{2 n}}$

(b) $\sqrt[3]{\frac{162}{6}}$

(c) $\sqrt[4]{\frac{160 r^{10}}{5 r^{3}}}$

Simplify:

a. ${(32 x^{\frac{1}{3}})}^{\frac{3}{5}}$ b. ${(x^{\frac{3}{4}} y^{\frac{1}{2}})}^{\frac{2}{3}}$

Use the Quotient Property to simplify square roots.

(a) $\sqrt{\frac{75 r^{6} s^{8}}{48 r s^{4}}}$

(b) $\sqrt[3]{\frac{24 x^{8} y 4}{81 x^{2} y}}$

(c) $\sqrt[4]{\frac{32 m^{9} n^{2}}{162 m n^{2}}}$

See all solutions

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