Book edition 6th

Author(s) Sullivan

Pages 1200 pages

ISBN 9780321795465

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Short Answer

In Problems 11–22, plot each complex number in the complex plane and write it in polar form. Express the argument in degrees.
$2 + \sqrt{3} i$ .

The polar form of $2 + \sqrt{3} i$ is, $\sqrt{7} (\cos 40 . 89^{\circ} + i \sin 40 . 89^{\circ})$ .

The given complex number is plotted in the complex plane.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1 Given argument is,

$2 + \sqrt{3} i$ .

The point corresponding to $z = 2 + \sqrt{3} i$ has the rectangular coordinates $(2, \sqrt{3})$ .

The point is located in the first quadrant and is plotted in the graph.

Step 2 The point is plotted in the graph and it is shown below.

Now from the co-ordinates of the point $P (2, \sqrt{3})$ we know that, $x = 2, y = \sqrt{3}$ .

Step 3 By using these values we can find out the polar coordinates, r and θ of the point P.

$r = \sqrt{x^{2} + y^{2}} = \sqrt{2^{2} + {(\sqrt{3})}^{2}} r = \sqrt{7}$

and,

$θ = \tan^{- 1} (\frac{y}{x}) = \tan^{- 1} (\frac{\sqrt{3}}{2}) = 40 . 89^{\circ}$

Hence the polar co-ordinates are $(\sqrt{7}, 40 . 89^{\circ})$ and in polar form it can be written as, $z = \sqrt{7} (\cos 40 . 89^{\circ} + i \sin 40 . 89^{\circ})$ .

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

In Problems 11–22, plot each complex number in the complex plane and write it in polar form. Express the argument in degrees.
$2 + \sqrt{3} i$ .

Step by Step Solution

Step 1 Given argument is,

Step 2 The point is plotted in the graph and it is shown below.

Step 3 By using these values we can find out the polar coordinates, r and θ of the point P.

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Step by Step Solution

Step 1 Given argument is,

Step 2 The point is plotted in the graph and it is shown below.

Step 3 By using these values we can find out the polar coordinates, r and θ of the point P.

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In Problems 11–22, plot each complex number in the complex plane and write it in polar form. Express the argument in degrees.
$2 + \sqrt{3} i$ .