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
First consider 100%. What is 100% of $40?
jenyasd209 [6]

Answer:

$40

Step-by-step explanation:

100% just means the whole, so 100% of $40 is $40.

5 0
3 years ago
A construction crew is building a two story house, but they have not built the staircase between the floor yet. The height of th
Naya [18.7K]

Answer:

13.4feet

Step-by-step explanation:

The set up forms a right triangle.

Given

Height of the staircase h = 12 feet

Base of the stairs b = 6feet

Required

Length of the ramp l

Using the pythagoras theorem

l² = h² + b²

l² = 12²+6²

l² = 144 + 36

l² = 180

l = √180

l = 13.42 feet

Hence the length of the ramp to the nearest tenth is 13.4feet

6 0
3 years ago
Doreen bought a cell phone for x dollars. One year later the value of the phone was 0.75x. Which expression is another way to de
OLEGan [10]

3/4x

0.75=75/100     =3/4

   75:25=3

100:25=4

6 0
3 years ago
The expanded fom of (a-b)²​
emmainna [20.7K]

Answer:

Step-by-step explanation:

(a-b)^{2} = a^{2} - 2ab + b^{2}

Hope this helps

plz mark as brainliest!!!!!

4 0
3 years ago
Read 2 more answers
A line that includes the points (-2,-7) and (-3, p) has a slope of -6. what is the value of p
MrRissso [65]

Answer:

p=-1

Step-by-step explanation:

y-y1=m(x-x1)

-7-p=-6(-2+3)

-7-p=-6

-p=1

p=-1

5 0
3 years ago
Other questions:
  • A youth Basketball has a standard Circumference of 27 inches. An NBA standard ball is 29.5 inches.
    10·1 answer
  • What is square root of -36?
    9·2 answers
  • A closet contains 5 pairs of pants, 7 shirts, and 3 pairs of shoes. How many leaves on a tree diagram would represent all possib
    7·2 answers
  • The 08:10 train from goblin's gap gets to mermaid's bay at ?
    14·2 answers
  • I need help with this problem 91+(-7)-5
    11·1 answer
  • A group of students bakes 100 cookies to sell at the school bake sale. The students want to ensure that the price of each cookie
    14·1 answer
  • Ira walked 20 miles last week and 22 miles this week. Raj walked 1/3 the distance that Ira walked. Write an expression for the d
    8·1 answer
  • By substituting
    6·1 answer
  • Meow help me pls :(((
    11·1 answer
  • Simplify the expression by combining like terms.
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!