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.
$- 2 + 3 i$ .

The polar form of $- 2 + 3 i$ is, $\sqrt{13} (\cos 123 . 7^{\circ} + i \sin 123 . 7^{\circ})$ .

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,

$- 2 + 3 i$ .

The rectangular co-ordinates of the point $(- 2 + 3 i)$ is, $(- 2, 3)$ .

Step 2 The point is plotted in the complex plane.

From the graph it is clear that the point is located in the first quadrant.

Step 3 We know that,

$|z| = r r = \sqrt{x^{2} + y^{2}} r = \sqrt{{(- 2)}^{2} + 3^{2}} r = \sqrt{13}$

Use $x = r \cos θ, y = r \sin θ$ to find the value of $θ$ .

$\sin θ = \frac{y}{r} = \frac{3}{\sqrt{13}} \cos θ = \frac{x}{r} = \frac{- 2}{\sqrt{13}}$

Since $\sin θ$ is $\frac{3}{\sqrt{13}}$ and $\cos θ = \frac{- 2}{\sqrt{13}}$ ,the value of $θ$ is, $123 . 7^{\circ}$ .

Step 4 The polar form of z=x+iy is, rcos θ+i sin θ.

The polar form of $- 2 + 3 i$ is, $\sqrt{13} (\cos 123 . 7^{\circ} + i \sin 123 . 7^{\circ})$ .

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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.
$- 2 + 3 i$ .

Step by Step Solution

Step 1 Given argument is,

Step 2 The point is plotted in the complex plane.

Step 3 We know that,

Step 4 The polar form of z=x+iy is, rcos θ+i sin θ.

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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+3i.

Step by Step Solution

Step 1 Given argument is,

Step 2 The point is plotted in the complex plane.

Step 3 We know that,

Step 4 The polar form of z=x+iy is, rcos θ+i sin θ.

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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.
$- 2 + 3 i$ .