Chapter 9: Q. 18 (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.
$9 \sqrt{3} + 9 i$

Short Answer

Expert verified

The plot is

the polar form is $z = 18 (\cos 30 ° + i \sin 30 °)$

Step by step solution

Given information

A complex number is given as $9 \sqrt{3} + 9 i$

Step 2. Plotting point

Let $x = 9 \sqrt{3} & y = 9 i$

Therefore the plot is

Step 3. Conversion into polar coordinates

The radius is

$r = \sqrt{x^{2} + y^{2}} = \sqrt{(9 \sqrt{3})^{2} + (9)^{2}} = 18$

And the argument is $θ = \tan^{- 1} (\frac{y}{x}) = \tan^{- 1} (\frac{9}{9 \sqrt{3}}) = 30 ° (as 0 \leq θ < 360 °)$

Therefore the polar coordinate is $(18, 30^{\circ})$

The polar form is $z = 18 (\cos 30 ° + i \sin 30 °)$

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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.
$9 \sqrt{3} + 9 i$

Short Answer

Step by step solution

Given information

Step 2. Plotting point

Step 3. Conversion into polar coordinates

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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.93+9i

Short Answer

Step by step solution

Given information

Step 2. Plotting point

Step 3. Conversion into polar coordinates

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Decision Maths

Probability and Statistics

Geometry

Calculus

Discrete Mathematics

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.
$9 \sqrt{3} + 9 i$