1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
soldier1979 [14.2K]
3 years ago
8

Which of the following statements about imaginary numbers are true? The square root of -1 is an imaginary number. is an imaginar

y number. i is an imaginary number. If an imaginary number is combined with a real number, the result is a complex number. Imaginary numbers aren’t practical
Mathematics
2 answers:
AveGali [126]3 years ago
7 0
All of those statements are true about imaginary numbers

Dmitry_Shevchenko [17]3 years ago
3 0

Answer:

The square root of -1 is an imaginary number: TRUE.

<em>i</em> is an imaginary number: TRUE.

If an imaginary number is combined with a real number, the result is a <em>complex number</em>: TRUE.

Imaginary numbers aren't practical: FALSE.

Step-by-step explanation:

<h3>First Part: \\ i = \sqrt{-1}</h3>

Imaginary numbers were the result of finding solutions for equations that require taking the square roots of negative numbers:

\\ \sqrt{-36} = \sqrt{-1*36} =\sqrt{-1} * \sqrt{36} = \sqrt{-1} *6 = 6i.

<em>Thus, the square root of -1 is an imaginary number</em>, and so \\ i since they are, in fact, the same: \\ i = \sqrt{-1}, which represents the <em>imaginary unit</em>. A consequence of that is \\ i^{2} = -1.

<h3>Second Part: a complex number is the result of combining an imaginary number with a real number.</h3>

A <em>complex number </em>is a quantity having <em>both a real and an imaginary part, </em>and are of the form<em> </em>\\ a + ib, since <em>imaginary numbers</em> <em>cannot</em> be represented on the <em>axis of real numbers</em>. They actually have their own axis called <em>imaginary axis</em>.

Both axes, then, form what is known as <em>complex plane</em> or <em>Argand diagram</em>, where <em>complex numbers</em> are represented.

In fact, a complex number with no real part is a <em>pure imaginary number</em>, and, conversely, a complex number with no imaginary number is a <em>pure real number</em>.  

<h3>Third Part: imaginary numbers are practical</h3>

Historically, Heaviside (1850-1925) "adapted complex numbers to the study of electrical circuits" [Wikipedia, 2019].

As a result, imaginary numbers are use to solve problems regarding electrical alternating current theory in <em>Electrical Engineering</em>, and they are represented by \\ j instead of \\ i, since \\ i is the symbol for electrical current.

There are many other applications on Quantum Mechanics, Dynamic Equations, signals analysis, control theory, fractal geometry, and so on.

Thus, imaginary numbers are use <em>in practice</em> to solve many problems in Science, Engineering, and Mathematics.

You might be interested in
Enrique is going to a party this weekend. He is bringing 20 liters of soda to the party. A liter of soda costs $1.59.
yulyashka [42]
It would be 31.80 because if you do 1.59 x 20 that will be the answer
8 0
3 years ago
(a) How many integers in the range 1 through 120 are integer multiples of 2, 3, or 5? keyboard_arrow_down Solution (b) How many
Umnica [9.8K]

Answer:

(a) 88 integers

(b) 92 integers

Step-by-step explanation:

(a) integers whose last digits are divisible by 2 are multiples of two or numbers whose digits ends with zero. So for number 1-120 , all the even numbers which are sixty in number are are multiples of two.

For  3, numbers whose digits sum is divisible by three are multiples of three. 3,6,9,12,15,18,21,24,27,30 are multiples of three from numbers 1-30. we have four 30s in 120. which means numbers of integers will be 10*4 = 40integers. However out of these numbers , half are also integers of 2 which reduces the number added to 20integers.

For 5, numbers whose digits ends with 5 or 0 are multiples of 5. this gives us 24 integers for 1-120. but out of these 24integers, 16 are common integers of 2 and 3 which reduces the number added to 8integers.

Thus from 1-120 the intergers of 2,3 or 5 = 60+20+8 = 88integers.

(b) if we are considering from numbers 1-140;

for 2 we wil have 70 integers,

for 5 we will have 28 integers, but those integers that end with 0 are also integers of 2 which reduces the number added to 14.

For 7, numbers 7,14,21,28,35,42,49,56,63,70 are multiples of three from 1-70. This pattern is repeated from number 71-140. hence we have 20 integers in all. However 12 of the multiples are also multiples of either 2 or 5 which reduces the number to 8 integers.

Thus from 1-140, the integers of 2, 5, or 7 = 70+14+8 = 92integers

3 0
3 years ago
What is the slope of the line shown below
Radda [10]

Here's the slope form; (y2- y1) / (x2 - x1)

All you have to do now is just plug in the number into the formula.

(6 - -4) / (6 - 1) = 10/5

Then divide, and the answer is D. 2.

3 0
4 years ago
Read 2 more answers
The potential energy, P, in a spring is represented using the formula P =1/2 kx2. Lupe uses an equivalent equation, which is sol
Kazeer [188]
The answer to this question will be K=2PX^2
4 0
3 years ago
Read 2 more answers
Help me!!!
Basile [38]

Answer:

this is your answer look it once.

8 0
3 years ago
Other questions:
  • Chad casts a shadow that is 14.3 feet long. The straight-line distance from the top of Chad’s head to the end of the shadow crea
    8·2 answers
  • A line passes through (2,-1) and (4,5). Which answer is the equation of the line?
    15·2 answers
  • What is <br> 0.24x − 1.85 3.09 − 2.33x  = 1.71
    14·1 answer
  • Considerando o diagrama, determine:
    14·1 answer
  • How to write 1/4 as a decimal with explanation
    15·1 answer
  • Let h(x)=2x+5hand g(x)=8-3xg, What is the value of h(g(1.5)
    8·1 answer
  • The first four terms in a linear sequence are shown below.
    15·1 answer
  • Please help asap! Will give brainliest! Please answer correctly!
    13·1 answer
  • Select the letter of the correct answer. A museum in South Africa uses paintings of right-angled triangles to teach children abo
    9·1 answer
  • Please Help!!!!!!!!!!
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!