Chapter 9: Q. 11 (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.
$1 + i$

Short Answer

Expert verified

The plot is

The polar form is $z = \sqrt{2} (\cos 45 ° + i \sin 45 °)$

Step by step solution

Step 1. Given information

Complex number is given as $1 + i$

Step 2. Plotting graph

Let $x = 1 & y = 1$

Plot the point as,

Step 3. Conversion to polar form

The radius is

$| z | = r = \sqrt{x^{2} + y^{2}} r = \sqrt{1^{2} + 1^{2}} = \sqrt{2}$

And the argument is

$\sin θ = \frac{y}{r} = \frac{1}{\sqrt{2}} \cos θ = \frac{x}{r} = \frac{1}{\sqrt{2}} \Rightarrow θ = 45^{\circ}$

The polar coordinate is $(\sqrt{2}, 45^{\circ})$

The polar form is

$z = r (\cos θ + i \sin θ) z = \sqrt{2} (\cos 45 ° + i \sin 45 °)$

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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.
$1 + i$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Plotting graph

Step 3. Conversion to polar form

One App. One Place for Learning.

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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.1+i

Short Answer

Step by step solution

Step 1. Given information

Step 2. Plotting graph

Step 3. Conversion to polar form

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Theoretical and Mathematical Physics

Decision Maths

Mechanics Maths

Pure Maths

Statistics

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.
$1 + i$