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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 426. (page 844)

In the following exercise, add.
$(- 3 + \sqrt{- 64}) + (5 - \sqrt{- 16})$

Short Answer

Expert verified

The value of the expression $(- 3 + \sqrt{- 64}) + (5 - \sqrt{- 16})$ is equal tolocalid="1645080244594" $\begin{array}{rcl} 2 + 4 i \end{array}$ .

Step by step solution

01

Step 1. Given information.

An expression is $(- 3 + \sqrt{- 64}) + (5 - \sqrt{- 16})$ .

02

Step 2. Add the complex numbers.

Consider the expression: $(- 3 + \sqrt{- 64}) + (5 - \sqrt{- 16})$

Use the square root of a negative number.

$\begin{array}{rcl} \sqrt{- 64} & = & 8 i \\ \sqrt{- 16} & = & 4 i \end{array}$

03

Step 3. Simplify the obtained value.

Apply the definition and substitute obtained values.

$\begin{array}{rcl} (- 3 + \sqrt{- 64}) + (5 - \sqrt{- 16}) & = & (- 3 + 8 i) + (5 - 4 i) \\ = & (- 3 + 5) + (8 i - 4 i) \\ = & 2 + 4 i \end{array}$

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