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Chapter 6: Q66. (page 293)

Simplify
$(7 + 2 i) (1 - i)$

Short Answer

Expert verified

The simplified value of expression is $(7 + 2 i) (1 - i) = 9 - 5 i$ .

Step by step solution

01

Step 1. Given Information.

Given to simplify the expression $(7 + 2 i) (1 - i)$

02

Step 2. Explanation.

From the properties of complex numbers, $i^{2} = - 1$

Using the above property,

$\begin{array}{l} (7 + 2 i) (1 - i) = 7 - 7 i + 2 i - 2 i^{2} \\ (7 + 2 i) (1 - i) = 7 - 7 i + 2 i - 2 (- 1) \\ (7 + 2 i) (1 - i) = 7 - 7 i + 2 i + 2 \\ (7 + 2 i) (1 - i) = 7 + 2 - 7 i + 2 i \\ (7 + 2 i) (1 - i) = 9 - 5 i \end{array}$

03

Step 3. Conclusion.

Therefore, The simplified value of expression is $(7 + 2 i) (1 - i) = 9 - 5 i$ .

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Most popular questions from this chapter

Steve has 120 feet of fence to make a rectangular kennel for his dogs. He will use his house as one side. What dimensions produce a kennel with the greatest area?

Use the related graph of each equation to determine its solutions.

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Solve each equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located.

$x^{2} + 4 x - 4 = 0$

Solve each equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are located.

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