Imaginary into real but not vice versa?

  • Thread starter aaryan0077
  • Start date
  • Tags
    Imaginary
In summary, the complex numbers allow for a simpler conversion from imaginary to real numbers through a basic operation like multiplication, while the reverse is not possible due to the more restrictive laws defining real numbers.
  • #1
aaryan0077
69
0
Its kinda weird (atleast to me) that we can convert imaginary numbers into real, there is just a simple procedure/function called multiplication. You multiply two no. and you get a real ,though negative. But not to worry we can still multiply it with 2 [tex]i's[/tex] or say [tex]i^2[/tex]. To make it positive.
But what about real numbers?
There is no such operation. Yeah, we can surely say that
[tex]2 =\frac{\ 2i}{i}[/tex] but this is not a satisfactory answer.
So why is there a way to imaginary to rela but not vice versa?
 
Mathematics news on Phys.org
  • #2
aaryan0077 said:
Its kinda weird (atleast to me) that we can convert imaginary numbers into real, there is just a simple procedure/function called multiplication. You multiply two no. and you get a real ,though negative. But not to worry we can still multiply it with 2 [tex]i's[/tex] or say [tex]i^2[/tex]. To make it positive.
But what about real numbers?
There is no such operation. Yeah, we can surely say that
[tex]2 =\frac{\ 2i}{i}[/tex] but this is not a satisfactory answer.
So why is there a way to imaginary to rela but not vice versa?

Quite simply because fewer laws/restrictions constitute the definition of the complex numbers than the reals, and that all the laws valid for complex numbers are valid for the reals as well.
That is, the reals can be regarded as a subset of the complex numbers, and "producible" from other complex numbers through an operation like multiplication.

Fully analogous is the case with rationals viz. integers with respect to the operation of multiplication:

It is impossible to multiply two integers and get a non-integer fraction, but 3/2*2/3, for example, equals the integer 2.
 
  • #3
The real numbers are "closed" under the usual arithmetic operations. The complex numbers are also but include the real numbers as a subset.
 

1. What does it mean to turn something imaginary into reality?

Turning something imaginary into reality means taking an idea or concept that exists only in the mind and making it a tangible, physical object or experience in the real world.

2. Can imaginary things ever truly become real?

Yes, imaginary things can become real, but it depends on the context. For example, a fictional character can never become a real person, but a technological innovation or scientific discovery can turn an imaginary concept into a real tool or solution.

3. Is it possible to turn an imaginary world into a real place?

In a literal sense, no, it is not possible to turn an imaginary world into a real place. However, elements or aspects of an imaginary world can be incorporated into real places through art, design, or technology.

4. How does imagination play a role in turning something into reality?

Imagination is the foundation for turning something into reality. It allows us to think beyond what currently exists and envision new possibilities. Without imagination, we would not have the drive or creativity to bring something imaginary into the real world.

5. Are there any risks or drawbacks to turning something imaginary into reality?

There can be risks or drawbacks to turning something imaginary into reality, depending on the specific situation. For example, if a fictional technology is brought to life without proper testing or consideration of potential consequences, it could have negative impacts. It is important to carefully assess and plan before attempting to make something imaginary into a reality.

Similar threads

Replies
36
Views
4K
  • General Math
Replies
29
Views
3K
Replies
7
Views
1K
Replies
28
Views
3K
Replies
3
Views
1K
Replies
3
Views
2K
Replies
3
Views
1K
  • General Math
Replies
6
Views
1K
Replies
1
Views
484
Replies
0
Views
594
Back
Top