Chapter 9: Q. 21 (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.
$- 2 + 3 i$ .

Short Answer

Expert verified

The polar form of $- 2 + 3 i$ is, $\sqrt{13} (\cos 123 . 7^{\circ} + i \sin 123 . 7^{\circ})$ .

The given complex number is plotted in the complex plane.

Step by step solution

Step 1 Given argument is,

$- 2 + 3 i$ .

The rectangular co-ordinates of the point $(- 2 + 3 i)$ is, $(- 2, 3)$ .

Step 2 The point is plotted in the complex plane.

From the graph it is clear that the point is located in the first quadrant.

Step 3 We know that,

$|z| = r r = \sqrt{x^{2} + y^{2}} r = \sqrt{{(- 2)}^{2} + 3^{2}} r = \sqrt{13}$

Use $x = r \cos θ, y = r \sin θ$ to find the value of $θ$ .

$\sin θ = \frac{y}{r} = \frac{3}{\sqrt{13}} \cos θ = \frac{x}{r} = \frac{- 2}{\sqrt{13}}$

Since $\sin θ$ is $\frac{3}{\sqrt{13}}$ and $\cos θ = \frac{- 2}{\sqrt{13}}$ ,the value of $θ$ is, $123 . 7^{\circ}$ .

Step 4 The polar form of z=x+iy is, rcos θ+i sin θ.

The polar form of $- 2 + 3 i$ is, $\sqrt{13} (\cos 123 . 7^{\circ} + i \sin 123 . 7^{\circ})$ .

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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.
$- 2 + 3 i$ .

Short Answer

Step by step solution

Step 1 Given argument is,

Step 2 The point is plotted in the complex plane.

Step 3 We know that,

Step 4 The polar form of z=x+iy is, rcos θ+i sin θ.

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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.-2+3i.

Short Answer

Step by step solution

Step 1 Given argument is,

Step 2 The point is plotted in the complex plane.

Step 3 We know that,

Step 4 The polar form of z=x+iy is, rcos θ+i sin θ.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Statistics

Theoretical and Mathematical Physics

Mechanics Maths

Geometry

Probability and 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.
$- 2 + 3 i$ .