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Chapter 8: Q53. (page 416)

Simplify the expression $(1 - 2 i) (2 + i)$ .

Short Answer

Expert verified

The simplified value of expression is $4 - 3 i$ .

Step by step solution

01

Step 1. Write down the given information.

The given expression is $(1 - 2 i) (2 + i)$ .

02

Step 2. Calculation.

Simplifying the given expression $(1 - 2 i) (2 + i)$ .

\begin{matrix} (1 - 2 i) (2 + i) = 1 (2 + i) - 2 i (2 + i) \\ = 2 + i - 4 i - 2 i^{2} \\ = 2 + i - 4 i - 2 (- 1) .... (∵ i^{2} = - 1) \\ = 2 - 3 i + 2 \\ = 4 - 3 i \end{matrix}

03

Step 3. Conclusion.

The simplified value of expression is $4 - 3 i$ .

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Most popular questions from this chapter

Identify the coordinates of the vertex and focus, the equations of the axis of symmetry and directrix, and the direction of opening of the parabola with the given equation $y = - 3 x^{2} - 8 x - 6$ . Then find the length of latus rectum and graph the parabola.

Which of the following point is closest to $(2, - 4)$ .

role="math" localid="1648203269021"

\begin{array}{l} (A) (3, 1) (B) (- 2, 0) \\ (C) (1, 5) (D) (4, - 2) \end{array}

Write an equation for each parabola described below. Then draw the graph.

vertex (4, 3), axis of symmetry x = 4, measure of latus rectum 4, a > 0.

Write the equation $y = \frac{1}{2} x^{2} + 12 x - 8$ in standard form.

Find the distance between the pair of points $(7, 8) and (- 4, 9)$ with the given coordinates.

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