Chapter 9: Q. 12 (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 $z = \sqrt{2} (\cos 135 ° + i \sin 135^{\circ})$

Step by step solution

Step 1. Given information

The complex number is given as $- 1 + i$

Step 2. Plotting point

Let $x = - 1 & y = 1$

Therefore the plot is

Step 3. conversion to polar form

The radius is

$r = \sqrt{x^{2} + y^{2}} = \sqrt{(- 1)^{2} + 1^{2}} = \sqrt{2}$

The argument is

$θ = \tan^{- 1} (\frac{y}{x}) = \tan^{- 1} (\frac{1}{(- 1)}) = 135 ° (as 0 \leq θ < 360 °)$

The polar coordinate is $(\sqrt{2}, 135^{\circ})$

The polar form is $z = \sqrt{2} (\cos 135 ° + i \sin 135^{'})$

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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 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.-1+i

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

Decision Maths

Statistics

Geometry

Calculus

Discrete Mathematics

Logic and Functions

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.
$- 1 + i$