Chapter 9: Q. 29 (page 592)

In Problems $23 - 32$ , write each complex number in rectangular form.
$0.2 (\cos 100^{\circ} + i \sin 100^{\circ})$ .

Short Answer

Expert verified

The rectangular form of the complex number $0.2 (\cos 100^{\circ} + i \sin 100^{\circ})$ is, $- 0.035 + 0.197 i$ .

Step by step solution

Step 1 Given complex number is,

$0.2 (\cos 100^{\circ} + i \sin 100^{\circ})$ .

The given complex number is in the form of $r (\cos θ + i \sin θ)$ where $x = r \cos θ, y = r \sin θ$ .

The $x$ co-ordinates of $0.2 (\cos 100^{\circ} + i \sin 100^{\circ})$ is,

$x = r \cos θ x = 0.2 \cos 100^{\circ} x = 0.2 (- 0.175) x = - 0.035$

Step 2 The y co-ordinate of 0.2cos 100∘+i sin 100∘ is,

$y = r \sin θ y = 0.2 \sin 100^{\circ} y = 0.2 (0.985) y = 0.197$

The rectangular form is, $z = x + i y z = - 0.035 + 0.197$

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In Problems $23 - 32$ , write each complex number in rectangular form.
$0.2 (\cos 100^{\circ} + i \sin 100^{\circ})$ .

Short Answer

Step by step solution

Step 1 Given complex number is,

Step 2 The y co-ordinate of 0.2cos 100∘+i sin 100∘ is,

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In Problems 23-32, write each complex number in rectangular form.0.2cos100∘+isin100∘.

Short Answer

Step by step solution

Step 1 Given complex number is,

Step 2 The y co-ordinate of 0.2cos 100∘+i sin 100∘ is,

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Decision Maths

Mechanics Maths

Geometry

Theoretical and Mathematical Physics

Logic and Functions

Study anywhere. Anytime. Across all devices.

In Problems $23 - 32$ , write each complex number in rectangular form.
$0.2 (\cos 100^{\circ} + i \sin 100^{\circ})$ .