Chapter 9: Q. 17 (page 630)

Write each complex number in the standard form $a + b i$ and plot each in the complex plane.
$\begin{array}{r} 3 (\cos \frac{2 π}{3} + i \sin \frac{2 π}{3}) \end{array}$

Short Answer

Expert verified

$z = \begin{array}{r} \frac{- 3}{2} + i \frac{3 \sqrt{3}}{2} \end{array}$

Step by step solution

Step 1. Given information

We have to write the given complex number in standard form. Also, we have to plot it in a complex plane.

Step 2. Convert the given complex number in standard form

To convert it in the standard form, we know that:

$z = x + i y = r (\cos θ + i \sin θ)$

For the given equation,

$\begin{aligned} z = 3 (\cos \frac{2 π}{3} + i \sin \frac{2 π}{3}) \\ = 3 (- \frac{1}{2} + i \frac{\sqrt{3}}{2}) \\ = \frac{- 3}{2} + i \frac{3 \sqrt{3}}{2} \end{aligned}$

Step 3. Plot the graph

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Write each complex number in the standard form $a + b i$ and plot each in the complex plane.
$\begin{array}{r} 3 (\cos \frac{2 π}{3} + i \sin \frac{2 π}{3}) \end{array}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Convert the given complex number in standard form

Step 3. Plot the graph

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Write each complex number in the standard form a+biand plot each in the complex plane.3cos⁡2π3+isin⁡2π3

Short Answer

Step by step solution

Step 1. Given information

Step 2. Convert the given complex number in standard form

Step 3. Plot the graph

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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Study anywhere. Anytime. Across all devices.

Write each complex number in the standard form $a + b i$ and plot each in the complex plane.
$\begin{array}{r} 3 (\cos \frac{2 π}{3} + i \sin \frac{2 π}{3}) \end{array}$