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labwork [276]
3 years ago
10

Locate the point in the complex plane and express the number in polar form.

Mathematics
1 answer:
EleoNora [17]3 years ago
4 0

Answer:

We kindly invite you to see the result in the image attached below.

The number in polar form is z = 3\sqrt{5}\cdot e^{i\cdot 0.352\pi}.

Step-by-step explanation:

A complex number is represented by elements of the form a + i\,b, for all a, b \in \mathbb{R}. The first part of the sum is the real component of the complex number, whereas the second part of the sum is the imaginary component of the complex number. The real component is located on the horizontal axis and the imaginary component on the vertical axis.

Now we proceed to present the point on the graph: (a = 6, b = 3)  We kindly invite you to see the result in the image attached below.

The polar form of the complex number is defined by:

z = r\cdot e^{i\cdot \theta} (1)

Where:

r - Magnitude of the complex number, dimensionless.

\theta - Direction of the complex number, measured in radians.

The magnitude and the direction of the complex number are defined by the following formulas:

Magnitude

r =\sqrt{a^{2}+b^{2}} (2)

Direction

\theta = \tan^{-1} \frac{b}{a} (3)

If we know that a = 6 and b = 3, then the polar form of the number is:

r =\sqrt{6^{2}+3^{2}}

r = 3\sqrt{5}

\theta = \tan^{-1} \frac{6}{3}

\theta \approx 0.352\pi \, rad

z = 3\sqrt{5}\cdot e^{i\cdot 0.352\pi}

The number in polar form is z = 3\sqrt{5}\cdot e^{i\cdot 0.352\pi}.

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r-ruslan [8.4K]

Answer:

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Step-by-step explanation:

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(10*3)

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5 0
3 years ago
The sum of 10 and Hector's age is 69 . Use the variable H to represent Hector's age.
mamaluj [8]

Answer:

59? Is it H = 59?

6 0
3 years ago
Create a word problem on Algebraic Expressions and Measurement (grade 10)​
mrs_skeptik [129]

Frank can build a fence in twice the time it would take Sandy. Working together, they can build it in 7 hours. How long will it take each of them to do it alone?

Answer

If Frank and Sandy can build the fence in 7 hours, they must be building

1

7

of the fence every hour.

Now, let the amount of time it takes Sandy be

x

hours so that Frank takes

2

x

hours. Sandy can build

1

x

of the fence every hour and Frank can build

1

2

x

of the fence every hour.

We now have the following equation to solve.

1

x

+

1

2

x

=

1

7

2

+

1

2

x

=

1

7

21

=

2

x

x

=

21

2

=

10.50

Thus, Sandy takes

10.50

hours and Frank takes

21

hours.

6 0
2 years ago
An instructor made a frequency table of the scores his students got on a test score frequency 30-under 40 1 40-under 50 4 50-und
RideAnS [48]
First, you add up the total number of students because we would base our percentage one this.

Total number of students = 1+4+5+10+20+10+5
Total number of students = 55

Now, let's count how many of them got a score of more than 70. For this, you would only count the students belonging to 70-under 80, 80-under 90 and 90-under 100.

Students who got more than 70 = 20+ 10 + 5 = 35

Therefore the percentage is equal to:
Percentage = 35/55 * 100 = 63.64%
4 0
3 years ago
I WILL AWARD BRAINLIEST!! PLEASE HELP!!
Marrrta [24]

Answer:

Fist one:

x−2=−3 

Second one: a=63b/23

Third one: x=−a/2+3b/2

7 0
3 years ago
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