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Imaginary numbers

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Jordan Vint
Jordan Vint

Imaginary numbers are square roots of negative real numbers that were introduced to allow taking the square root of negatives. An example of an imaginary number is 2i√6, where i represents the imaginary unit. Imaginary numbers can be added, subtracted, multiplied, and divided like real numbers. When squared, imaginary numbers follow a repeating sequence of i, -1, -i, 1. Though sometimes complex, imaginary numbers serve an important purpose and are generally easy to work with through practice and logical thinking.

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Imaginary NumbersA How To by Jordan Vint.
A Quick DefinitionAn Imaginary number. Abbreviated by ‘I’. Is indeed a fake number. And is the square root of a real negative number. It was introduced in mathematics for the sole purpose of allowing people take square roots of negative numbers.It was originally impossible to do such a thing. As it can’t be done when you limit yourself to real numbers.
A Quick ExampleLet’s see. Imagine this. You’ve a negative number and decide you want to square root it. We’ll use 24. So if I knew how to use the square root symbol I’d show you. But it would come out as [-24]24’s not a perfect square. So you’d have to find either a perfect or normal square that could go into it.A perfect square that can go into it would be 4 which when multiplied by 6 would equal 24.So what could be written is 4i[6] with the I representing the imaginary number which is 4. However that’s not the end. 4’s a perfect square and as such can be rounded down to 2.So the final solution would show up as 2i[6]. With the two under the root symbol it cannot be changed therefore it stays the same.
Complex NumbersLike real numbers. Imaginary numbers can be used in multiplication through division. They’re generally rather simple. But some can get a bit tricky. Depending on their length.Here’s an example. (6+3i) + (8+9i) The I represents imaginary numbers once again. And when adding like this it’s a simple matter of like terms. (14+12i).Another example: (7+9i) – (11+3i) = (-4+6i)
Continued.Imaginary numbers. Being square roots of negative numbers. Can have different effects on problems and positive numbers. For example: i= -1 squared. i^2 = -squared to the second power. Which would come to equal negative one which could then be multiplied into the problem affecting whether it could be negative or positive. Imaginaries can also be multiplied through the box formula. Which involves putting the two sequences of numbers into a box. Multiplying them out. And then adding like terms to find the final solution.It may sound complicated. But it’s quite simple.
Finishing OffImaginaries when squared follow a sequence.Example: i=i. i^2=-1. i^3=-i. And i^4=1. And it continues in that sequence forever. (i^5+7i^2)(9i^3-2i^1) = 11 + 77i.In laymen’s terms. Imaginary numbers were made with a good purpose. And are quite easy to work with. There are occasional tough ones but they can generally be solved with a good deal of thinking.

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Imaginary numbers

  • 1. Imaginary NumbersA How To by Jordan Vint.
  • 2. A Quick DefinitionAn Imaginary number. Abbreviated by ‘I’. Is indeed a fake number. And is the square root of a real negative number. It was introduced in mathematics for the sole purpose of allowing people take square roots of negative numbers.It was originally impossible to do such a thing. As it can’t be done when you limit yourself to real numbers.
  • 3. A Quick ExampleLet’s see. Imagine this. You’ve a negative number and decide you want to square root it. We’ll use 24. So if I knew how to use the square root symbol I’d show you. But it would come out as [-24]24’s not a perfect square. So you’d have to find either a perfect or normal square that could go into it.A perfect square that can go into it would be 4 which when multiplied by 6 would equal 24.So what could be written is 4i[6] with the I representing the imaginary number which is 4. However that’s not the end. 4’s a perfect square and as such can be rounded down to 2.So the final solution would show up as 2i[6]. With the two under the root symbol it cannot be changed therefore it stays the same.
  • 4. Complex NumbersLike real numbers. Imaginary numbers can be used in multiplication through division. They’re generally rather simple. But some can get a bit tricky. Depending on their length.Here’s an example. (6+3i) + (8+9i) The I represents imaginary numbers once again. And when adding like this it’s a simple matter of like terms. (14+12i).Another example: (7+9i) – (11+3i) = (-4+6i)
  • 5. Continued.Imaginary numbers. Being square roots of negative numbers. Can have different effects on problems and positive numbers. For example: i= -1 squared. i^2 = -squared to the second power. Which would come to equal negative one which could then be multiplied into the problem affecting whether it could be negative or positive. Imaginaries can also be multiplied through the box formula. Which involves putting the two sequences of numbers into a box. Multiplying them out. And then adding like terms to find the final solution.It may sound complicated. But it’s quite simple.
  • 6. Finishing OffImaginaries when squared follow a sequence.Example: i=i. i^2=-1. i^3=-i. And i^4=1. And it continues in that sequence forever. (i^5+7i^2)(9i^3-2i^1) = 11 + 77i.In laymen’s terms. Imaginary numbers were made with a good purpose. And are quite easy to work with. There are occasional tough ones but they can generally be solved with a good deal of thinking.