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 $z = 4 \sqrt{2} (\cos 315 ° + i \sin 315 °)$

Step by step solution

Step 1. Given information

Complex number is given as $4 - 4 i$

Step 2. Plotting point

Let $x = 4 & y = - 4$

Therefore the plot is

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

$\sin θ = \frac{y}{r} = \frac{- 4}{4 \sqrt{2}} = \frac{- 1}{\sqrt{2}} \cos θ = \frac{x}{r} = \frac{4}{4 \sqrt{2}} = \frac{1}{\sqrt{2}} \Rightarrow θ = 135^{\circ}$

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

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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.
$4 - 4 i$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Plotting point

Step 3. Conversion to polar form

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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.4-4i

Short Answer

Step by step solution

Step 1. Given information

Step 2. Plotting point

Step 3. Conversion to polar form

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Pure Maths

Probability and Statistics

Geometry

Applied Mathematics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

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