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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. 11 (page 631)

In Problems 10鈥�12, perform the given operation, where $z = 2 (\cos 85 掳 + i \sin 85 掳)$ and $w = 3 (\cos 22 掳 + i \sin 22 掳)$ . Write your answer in polar form.
$\frac{w}{z}$

Short Answer

Expert verified

The answer is $\frac{w}{z} = \frac{3}{2} (\cos 297 掳 + i \sin 297 掳)$

Step by step solution

01

Step 1. Given information

We have been given $z = 2 (\cos 85 掳 + i \sin 85 掳)$ and $w = 3 (\cos 22 掳 + i \sin 22 掳)$ .

We have to perform the operation $\frac{w}{z}$

02

Step 2. Perform the operation

$\frac{w}{z} = \frac{3 (\cos 22 掳 + i \sin 22 掳)}{2 (\cos 85 掳 + i \sin 85 掳)} = \frac{3}{2} [\cos (22 掳 - 85 掳) + i \sin (22 掳 - 85 掳)] = \frac{3}{2} (\cos (- 63 掳) + i \sin (- 63 掳)) = \frac{3}{2} (\cos (360 掳 - 63 掳) + i \sin (360 掳 - 63 掳)) = \frac{3}{2} (\cos 297 掳 + i \sin 297 掳)$

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Most popular questions from this chapter

In Problems 13鈥�28, transform each polar equation to an equation in rectangular coordinates. Then identify and graph the equation. Verify your graph using a graphing utility.

$r = 2$

Match the graph with the polar equation.

$r = 2 \sin 胃$

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

$r = 2 - 3 \cos 胃$

In Problems 11鈥�22, plot each complex number in the complex plane and write it in polar form. Express the argument in degrees.

$3 - 4 i$ .

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

${[3 (\cos 80 掳 + i \sin 80 掳)]}^{3}$

See all solutions

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