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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 427. (page 844)

In the following exercise, subtract.
$(- 7 - \sqrt{- 50}) - (- 32 - \sqrt{- 18})$

Short Answer

Expert verified

The value of the expression $(- 7 - \sqrt{- 50}) - (- 32 - \sqrt{- 18})$ is $\begin{array}{rcl} 25 - 2 \sqrt{2} i \end{array}$ .

Step by step solution

01

Step 1. Given information.

An expression is $(- 7 - \sqrt{- 50}) - (- 32 - \sqrt{- 18})$ .

02

Step 2. Subtract the complex numbers.

Use the square root of a negative number.

$\sqrt{- 50} = 5 \sqrt{2} i \sqrt{- 18} = 3 \sqrt{2} i$

03

Step 3. Simplify the obtained value.

Apply the definition and substitute obtained values.

$\begin{array}{rcl} (- 7 - \sqrt{- 50}) - (- 32 - \sqrt{- 18}) & = & (- 7 - 5 \sqrt{2} i) - (- 32 - 3 \sqrt{2} i) \\ = & - 7 - 5 \sqrt{2} i + 32 + 3 \sqrt{2} i \\ = & (- 7 + 32) + (- 5 \sqrt{2} i + 3 \sqrt{2} i) \\ = & 25 - 2 \sqrt{2} i \end{array}$

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