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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. 17 (page 591)

In Problems $11 - 22$ , plot each complex number in the complex plane and write it in polar form. Express the argument in degrees.
$4 - 4 i$

Short Answer

Expert verified

The plot is

The polar form is $z = 4 \sqrt{2} (\cos 315 掳 + i \sin 315 掳)$

Step by step solution

01

Step 1. Given information

Complex number is given as $4 - 4 i$

02

Step 2. Plotting point

Let $x = 4 & y = - 4$

Therefore the plot is

03

Step 3. Conversion to polar form

The radius is

$| z | = r = \sqrt{x^{2} + y^{2}} r = \sqrt{4^{2} + (- 4)^{2}} = \sqrt{16 + 16} = \sqrt{32} = 4 \sqrt{2}$

The angle is

$\sin 胃 = \frac{y}{r} = \frac{- 4}{4 \sqrt{2}} = \frac{- 1}{\sqrt{2}} \cos 胃 = \frac{x}{r} = \frac{4}{4 \sqrt{2}} = \frac{1}{\sqrt{2}} 鈬� 胃 = 135^{鈭�}$

The polar form is $z = r (\cos 胃 + i \sin 胃) z = 4 \sqrt{2} (\cos 315 掳 + i \sin 315 掳)$

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Most popular questions from this chapter

Write the expression in the standard form $a + i b$ .

${[3 (\cos 80 掳 + i \sin 80 掳)]}^{3}$

If $\overset{鈬赌}{v} = 2 \overset{鈬赌}{i} - \overset{鈬赌}{j}$ and $\overset{鈬赌}{w} = x \overset{鈬赌}{i} + 3 \overset{鈬赌}{j}$ , find all numbers x for which $|\overset{鈬赌}{v} + \overset{鈬赌}{w}| = 5$ .

The standard equation of a circle with center at $(- 2, 5)$ and radius $3$ is ______ .

In Problems, the vector v has initial point P and terminal point Q. Write v in the form ai + bj; that is, find its position vector.

$P = (3, 2); Q = (5, 6)$

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

$r^{2} = \sin (2 胃)$

See all solutions

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