Chapter 9: Q. 38 (page 592)

In Problems $33 - 40$ , find $z w$ and $\frac{z}{w}$ .Leave your answers in polar form.
$z = 4 (\cos \frac{3 π}{8} + i \sin \frac{3 π}{8}) w = 2 (\cos \frac{9 π}{16} + i \sin \frac{9 π}{16})$

Short Answer

Expert verified

The polar form of $z w$ is, $8 (\cos \frac{15 π}{16} + i \sin \frac{15 π}{16})$ .

The polar form of $\frac{z}{w}$ is, $2 (\cos \frac{3 π}{16} - i \sin \frac{3 π}{16})$ .

Step by step solution

Step 1 Given that,

$z = 4 (\cos \frac{3 π}{8} + i \sin \frac{3 π}{8}) w = 2 (\cos \frac{9 π}{16} + i \sin \frac{9 π}{16})$

First find $z w$ .

$z . w = 4 (\cos \frac{3 π}{8} + i \sin \frac{3 π}{8}) . 2 (\cos \frac{9 π}{16} + i \sin \frac{9 π}{16}) = 8 (\cos (\frac{3 π}{8} + \frac{9 π}{16}) + i \sin (\frac{3 π}{8} + \frac{9 π}{16})) = 8 (\cos (\frac{6 π + 9 π}{16}) + i \sin (\frac{6 π + 9 π}{16})) = 8 (\cos \frac{15 π}{16} + i \sin \frac{15 π}{16})$

Step 2 Next find zw.

$\frac{z}{w} = \frac{4 (\cos \frac{3 π}{8} + i \sin \frac{3 π}{8})}{2 (\cos \frac{9 π}{16} + i \sin \frac{9 π}{16})} = 2 [\cos (\frac{3 π}{8} - \frac{9 π}{16}) + i \sin (\frac{3 π}{8} - \frac{9 π}{16})] = 2 [\cos (\frac{6 π - 9 π}{16}) + i \sin (\frac{6 π - 9 π}{16})] = 2 [\cos (\frac{- 3 π}{16}) + i \sin (\frac{- 3 π}{16})]$

We know that,

\cos (- θ) = \cos θ \sin (- θ) = - \sin θ

Thus,

$\frac{z}{w} = 2 [\cos (\frac{3 π}{16}) - i \sin (\frac{3 π}{16})]$

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In Problems $33 - 40$ , find $z w$ and $\frac{z}{w}$ .Leave your answers in polar form.
$z = 4 (\cos \frac{3 π}{8} + i \sin \frac{3 π}{8}) w = 2 (\cos \frac{9 π}{16} + i \sin \frac{9 π}{16})$

Short Answer

Step by step solution

Step 1 Given that,

Step 2 Next find zw.

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In Problems 33-40, find zwand zw.Leave your answers in polar form.z=4cos3π8+isin3π8w=2cos9π16+isin9π16

Short Answer

Step by step solution

Step 1 Given that,

Step 2 Next find zw.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Discrete Mathematics

Probability and Statistics

Logic and Functions

Pure Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In Problems $33 - 40$ , find $z w$ and $\frac{z}{w}$ .Leave your answers in polar form.
$z = 4 (\cos \frac{3 π}{8} + i \sin \frac{3 π}{8}) w = 2 (\cos \frac{9 π}{16} + i \sin \frac{9 π}{16})$