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
arlik [135]
3 years ago
9

I will give you brainliest, if you provide an accurate explanation.

Mathematics
2 answers:
Molodets [167]3 years ago
8 0

Answer:

sqrt(i) =0.707106781 + 0.707106781 i

Most of the numbers we know, and work with, are Real Numbers. The Real Number System includes counting numbers, fractions, terminating decimals, positive numbers, negative numbers, zero, repeating decimals, never ending and non-repeating decimals, numbers that are expressed as radicals, and even pi (π).

The natural numbers are the set of counting numbers

• There are infinitely many numbers in a set of numbers.

• The natural numbers are "closed" under addition and multiplication.

The addition of two natural numbers creates another natural number.

The multiplication of two natural numbers creates another natural number.

closed under addition and multiplication.

BUT ...

The subtraction of two natural numbers does NOT necessarily create another natural number

The division of two natural numbers does NOT necessarily create another natural number  

The whole numbers are the set of counting numbers (natural numbers) along with zero

   

• There are infinitely many numbers in this set of numbers.

• The set of whole numbers is "closed" under addition and multiplication.

Integers:

• The integers are the set of all of the natural numbers,

    plus their additive inverses and zero

• The integers are "closed" under addition, multiplication and subtraction,

    but NOT under division

Rational Numbers:

• The rational numbers are the set of numbers which can be expressed as a ratio

    (a fraction) between two integers.

• Integers are rational numbers since 5 can be written as the fraction 5/1.

• Decimals which terminate are rational numbers.

• Decimals which have a repeating pattern are rational numbers. 1/3 = 0.3333333...

• The rational numbers are "closed" under addition, subtraction, and multiplication. Under division, we run into the problem of division by 0, which makes the statement that "the rationals are closed under division" false. Some texts state that "the rationals are closed under division as long as the division is not by zero" which is a true statement.

Irrational Numbers:

The irrational numbers are the set of number which can NOT be written as a ratio (fraction).

• Decimals which never end nor repeat are irrational numbers.

• Irrational numbers are "not closed" under addition, subtraction, multiplication or division.

• Examples of irrational numbers: rad2, π

Vera_Pavlovna [14]3 years ago
7 0

This is figured out by first figuring out that:

√(√(i)) = i^{1/4\\}

Let \sqrt{i} be a + bi.

Square both sides to get i = (a + bi)(a + bi)

So, i = a² - b² + 2abi

a² - b² is the real part. The real part is 0.

0 + i = a² - b² + 2abi

a² - b² = 0

i = 2abi

2ab = 1

ab = 1/2

b = 1/2a

Now, since a² - b² = 0,

a² - (1/2a)² = 0

a² - 1/(4a²) = 0

\frac{(4a^{4}-1 )}{4a^{2} } = 0

That means the numerator MUST be 0.

(4a^{4}-1 )} = 0

4a^{4} = 1

a^{4} = 1/4

a = ± \frac{1}{\sqrt{2} }

if a = \frac{1}{\sqrt{2} } , then b = \frac{1}{\sqrt{2} }

If a = -\frac{1}{\sqrt{2} } , then b = -\frac{1}{\sqrt{2} }

So, it's either a = -\frac{1}{\sqrt{2} }  and b = -\frac{1}{\sqrt{2} } , or a = \frac{1}{\sqrt{2} }  and b = \frac{1}{\sqrt{2} }

That's why sqrt(i) =0.707106781 + 0.707106781i, or sqrt(i) = -0.707106781 - 0.707106781i

You might be interested in
It costs twelve dollars to get in to the fair. Tickets for rides cost extra and are d dollars each,
atroni [7]
I think it’s 20d-$12
Hope this helps!
6 0
3 years ago
1.. If a golfer’s score of 4 under par is represented by –4 on a number line, then how would a golfers score of 4 over par best
olya-2409 [2.1K]
This is a bit of a guess, but I think probably a) +4 and also a) -215
3 0
3 years ago
I need help with my assignment but dont know how to do it/ what should i do?
ohaa [14]

Answer:

first explain what you need help with specifically then maybe people can help, to bland of a question

5 0
3 years ago
Slove system of equation.<br><br> 2x - 6y = 8<br> -3x + 9y = 12
Bond [772]
Answers:

2x - 6y = 8 -> x = 4 + 3y

-3x + 9y = 12 -> x = -4 + 3y
7 0
2 years ago
What are the measures of Angles a, b, and c? Show your work and explain your answers.
jolli1 [7]
Answer: a = 40, b = 50, c = 115

Solution:
a = 40 (the vertical angles are equal)

b = 180 - 40 - a = 50 (the sum of interior angles of triangle is 180)

c = 180 - 65 = 115 (the linear theorem)
5 0
2 years ago
Other questions:
  • At westwood Middleschool, 648 students responded to a survey asking about their favorite type of exercise. Twice as many student
    10·1 answer
  • For the function f defined by f(x)=5x−12 find f(−x),−f(x), and −f(−x).
    15·1 answer
  • What are the values of cos α and tan α, if: sinα= 40/41
    10·1 answer
  • Quan bought 8.6 meters of fabric.how many centimeters of fabric did he buy
    6·1 answer
  • What is the remainder when x^2+5 is divided by x+1?
    15·1 answer
  • The altitude to the hypotenuse of a right triangle divides the hypotenuse into segments 2 cm and 8 cm long. ​Find the length of
    5·1 answer
  • Solve for x in the triangle. round your answer to the nearest tenth
    7·1 answer
  • The numbers 1-11 are placed in a bag. What is the probability of drawing a prime number?
    5·2 answers
  • The difference of two numbers is 4. Their sum is 18. Find the numbers.
    5·2 answers
  • Which of the following are solutions to the graph
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!