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oksian1 [2.3K]
3 years ago
5

Simplify the given expression below: 4 divided by the quantity of 3 minus 2i

Mathematics
2 answers:
svetoff [14.1K]3 years ago
3 0
This is rationalising the denominator of an imaginary fraction. We want to remove all i's from the denominator.

To do this, we multiply the fraction by 1. However 1 can be expressed in an infinite number of ways. For example, 1 = 2/2 = 3/3 = 4n^2 / 4n^2 (assuming n is not zero!). Let's express 1 as the complex conjugate of the denominator, divided by the complex conjugate of the denominator.

The complex conjugate of (3 - 2i) is (3 + 2i). Then do what I just said:

4/(3-2i) * (3+2i)/(3+2i) = 4(3+2i)/(3-2i)(3+2i) = (12+8i)/(9-4i^2) = (12+8i)/(9+4) = (12+8i)/13

This is the answer you are looking for. I hope this helps :)
vova2212 [387]3 years ago
3 0

Answer:

4/(3-2i) * (3+2i)/(3+2i) = 4(3+2i)/(3-2i)(3+2i) = (12+8i)/(9-4i^2) = (12+8i)/(9+4) = (12+8i)/13

Step-by-step explanation:

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✎Question:Amirah is 4 years elder than Priya and Shirley is 2 years younger than Priya. If the sum of their ages is 47, find the
Gnom [1K]

Answer:

Priya's age = 15

Amirah's age = 19

Shirley's age = 13

Step-by-step explanation:

Let x be the age of Priya.

According to the question,

Amirah's age = x + 4

Shirley's age = x - 2

Their sum is 47.

So,

x + 4 + x + x - 2 = 47

3x + 2 = 47

3x = 47 - 2

3x = 45

x = 45/3

x = 15

So,

Priya's age = 15

Amirah's age = 15 + 4 = 19

Shirley's age = 15 - 2 = 13

7 0
3 years ago
Read 2 more answers
The area of a rectangle with width × and length 7× is 7². what does the coefficient 7 mean in terms of the problem?
tatuchka [14]

The coefficient 7 means that the length is 7 times the width

<h3>How to interpret the coefficient?</h3>

The given parameters are:

Width = x

Length = 7x

Area = 7x^2

We have:

Length = 7x

Substitute Width = x in Length = 7x

Length = 7 * Width

This means that the length is 7 times the width

Read more about areas at:

brainly.com/question/14137384

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5 0
2 years ago
Prove the triangles are congruent
frozen [14]

Answer:

1: two sides and angle of one triangle are congruent.

Step-by-step explanation:

The triangles are congruent because two sides and the generated angle of a triangle correspond to their respective sections. If two angles and the side used in one triangle are identical.

Hope this helps

4 0
3 years ago
An airline allows each passenger 33 kilograms of luggage. Carl has to lower the weight of his suitcase by 25% to stay within the
damaskus [11]
1- 0.25= 0.75 (multiplier)

33÷0.75=44

The suitcase originally weighed 44kg

Hope this helps!
5 0
3 years ago
Read 2 more answers
Jen picked 3/4 of a gallon of strawberries in a half an hour.If she keeps picking strawberries at the same rate, how many gallon
sp2606 [1]

Answer:

3 gallons.

Step-by-step explanation:

We have been given that Jen picked 3/4 of a gallon of strawberries in a half an hour.

Let us convert our given time in minutes.

1 hour= 60 minutes.

1/2 hour= 30 minutes.

So 2 hours= 120 minutes.

Let us find the number of gallons of strawberries picked by Jen in 30 minutes by dividing 3/4 by 30.

\text{The number of gallons of strawberries picked by Jen in 30 minutes}=\frac{\frac{3}{4} }{30}

\text{The number of gallons of strawberries picked by Jen in 30 minutes}=\frac{3}{4*30}

\text{The number of gallons of strawberries picked by Jen in 30 minutes}=\frac{1}{40}

Now let us multiply 1/40 by 120 to find the number of gallons of strawberries picked by Jen in 120 minutes(2 hours).

\text{The number of gallons of strawberries picked by Jen in 30 minutes}=120*\frac{1}{40}

\text{The number of gallons of strawberries picked by Jen in 30 minutes}=3

Therefore, Jen picked 3 gallons of strawberries in 2 hours.

8 0
3 years ago
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