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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 9: Q. 31 (page 592)

In Problems $23 - 32$ , write each complex number in rectangular form.
$2 (\cos \frac{蟺}{18} + i \sin \frac{蟺}{18})$ .

Short Answer

Expert verified

The rectangular form of the complex number $2 (\cos \frac{蟺}{18} + i \sin \frac{蟺}{18})$ is, $1.970 + 0.347 i$ .

Step by step solution

01

Step 1 Given complex number is,

$2 (\cos \frac{蟺}{18} + i \sin \frac{蟺}{18})$ .

The given complex number is in the form of $r (\cos 胃 + i \sin 胃)$ where $x = r \cos 胃, y = r \sin 胃$ .

The $x$ co-ordinates of $2 (\cos \frac{蟺}{18} + i \sin \frac{蟺}{18})$ is,

$x = r \cos 胃 x = 2 \cos \frac{蟺}{18} x = 2 (0.985) x = 1.970$

02

Step 2 The y co-ordinate of 2cos π18+i sin π18 is,

$y = r \sin 胃 y = 2 \sin (\frac{蟺}{18}) y = 2 (0.1735) y = 0.347$

Thus the rectangular form is,

role="math" localid="1646758961916" $z = x + i y z = 1.970 + 0.347 i$

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Most popular questions from this chapter

Identify and graph each polar equation. Verify your graph using a graphing utility.

$r = 4 \cos (3 胃)$

Find a vector $v$ whose magnitude is $4$ and whose component

in the $i$ direction is twice the component in the $j$ direction.

Identify and graph each polar equation. Verify your graph using a graphing utility

$r = 3 - 3 \sin 胃$

Match the graph with the polar equation

$r \sin 胃 = 2$

Explain how you proceed to convert from rectangular coordinates to polar coordinates.

See all solutions

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