Chapter 9: Q. 15 (page 630)

Write each complex number in polar form. Express each argument in degrees.
$4 - 3 i$

Short Answer

Expert verified

The polar form of $z = 4 - 3 i$ is $5 (\cos 323 . 1^{o} + i \sin 323 . 1^{o})$

Step by step solution

Step 1. Given data

$z = 4 - 3 i$

Step 2. Calculate the distance r

The polar form of $z = x + i y$ is $z = r (\cos θ + i \sin θ)$

We know,

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

Substituting the values of (x, y)=(4, -3),

$r = \sqrt{{(4)}^{2} + {(- 3)}^{2}}$

$r = \sqrt{16 + 9}$

$r = \sqrt{25}$

$r = 5$

Step 3. Calculating the value of θ

Substitute $x = r \cos θ$ and $y = r \sin θ$ ,

$\sin θ = \frac{y}{r} = \frac{- 3}{5}$ and $\cos θ = \frac{4}{5}$

Since, $\sin 323 . 1^{o} = \frac{- 3}{5}$ and $\cos 323 . 1^{0} = \frac{4}{5}$ .

Therefore, the polar form of $z = 4 - 3 i$ is $5 (\cos 323 . 1^{o} + i \sin 323 . 1^{o})$

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Write each complex number in polar form. Express each argument in degrees.
$4 - 3 i$

Short Answer

Step by step solution

Step 1. Given data

Step 2. Calculate the distance r

Step 3. Calculating the value of θ

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Write each complex number in polar form. Express each argument in degrees.4-3i

Short Answer

Step by step solution

Step 1. Given data

Step 2. Calculate the distance r

Step 3. Calculating the value of θ

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Discrete Mathematics

Decision Maths

Applied Mathematics

Theoretical and Mathematical Physics

Logic and Functions

Study anywhere. Anytime. Across all devices.

Write each complex number in polar form. Express each argument in degrees.
$4 - 3 i$