Learn about the imaginary unit i, about the imaginary numbers, and about square roots of negative numbers.

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Dlnickelson17

8 years agoPosted 8 years ago. Direct link to Dlnickelson17's post “what would -i^-i be, woul...”

what would -i^-i be, would it just be 2^2

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(114 votes)

ArjanK

2 years agoPosted 2 years ago. Direct link to ArjanK's post “it would be i^3(i^3) = -1...”

it would be i^3(i^3) = -1^(-1) = 1/-1 = -1

(20 votes)

Michael Mendoza

8 years agoPosted 8 years ago. Direct link to Michael Mendoza's post “What is the real world ap...”

What is the real world application for this??

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(73 votes)

kurt westphal

8 years agoPosted 8 years ago. Direct link to kurt westphal's post “design, simulation, analy...”

design, simulation, analysis of normal and semiconductor circuits, acoustics and speakers, physics., mechanical system vibration, automotive exhaust note tuning, guitar pickups and boutique high power tube/solid state amplifiers, chemical engineering linear/non linear flows, financial modeling, statistics and big data,

(238 votes)

Vestige

a year agoPosted a year ago. Direct link to Vestige's post “my brain blew up”

my brain blew up

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(83 votes)

oliver.wagner

a year agoPosted a year ago. Direct link to oliver.wagner's post “the brain can not blow up...”

the brain can not blow up unless it was overloaded with knowlege

(66 votes)

Mojeb Rahman Zameeri

a year agoPosted a year ago. Direct link to Mojeb Rahman Zameeri's post “hard to believe there are...”

hard to believe there are people out there that imagine numbers

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(50 votes)

Aeternum

a year agoPosted a year ago. Direct link to Aeternum's post “Technically, numbers and ...”

Technically, numbers and mathematics in general are all imaginary. Mathematics is not a physical object that literally exists in the seeable universe. It, like numbers, was made up by humanity.

(57 votes)

Syeda5

7 years agoPosted 7 years ago. Direct link to Syeda5's post “If imaginary numbers aren...”

If imaginary numbers aren't real, how is it possible to use them in real life? You can't count things that don't exist so how do you use them?

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(8 votes)

kubleeka

7 years agoPosted 7 years ago. Direct link to kubleeka's post “None of the numbers you u...”

None of the numbers you use in life are real. Can you show me a 3? Not a drawing or a representation of a 3, but the actual number 3? Of course not. It's just an abstraction.

You mention counting, but most numbers aren't used for counting either. You can't have exactly √2 apples, or any irrational number of apples. That would require splitting atoms and quarks in impossible ways. Yet a vast majority of the real numbers are irrational. They're not about counting either.

Numbers are just concepts that follow certain rules. The misleadingly-named real numbers are defined as a complete ordered field. The word "field" just means that they follow 9 certain rules, like "for every real number x, x+0=x" Likewise, "ordered" just adds about 3 more rules, and "complete" adds one more. Any relation to real life is just the result of people applying these abstractions to real-world problems.

To get the complex numbers, we do a similar thing. Take the real numbers and add in

1. Every real number is complex.

2. There is a complex number i such that i²= -1.

3. The sum of two complex numbers is complex.

4. The product of two complex numbers is complex.

5. For any two complex numbers a and b, a^b is complex.Now we have this concept of "the complex numbers" that we can further explore. Application to reality is not necessary.

(72 votes)

Daisy Dukealoopakiss

8 years agoPosted 8 years ago. Direct link to Daisy Dukealoopakiss's post “Can you have different an...”

Can you have different answers to simplifying depending on what numbers you take from the original, or would those be wrong? For example: Problem 3, instead of using 4 and 6 I used 8 and 3 and it came out to be 2i x square of 2 x square of 2 x square of 3, but it was counted as wrong. Was it wrong because it wasn't what Kahn had, or because it was just wrong?

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(22 votes)

jesse.l.kent

8 years agoPosted 8 years ago. Direct link to jesse.l.kent's post “They were asking for the ...”

They were asking for the square root. The square root of 4 is 2 so you would have 2i sqrt(6) ... The cubed root of 8 is 2 not the square root.

(38 votes)

27svinay

a year agoPosted a year ago. Direct link to 27svinay's post “How would one use an imag...”

How would one use an imaginary number in real life? If it is imaginary, would it have any use cases? If so, how exactly would you need to use it?

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(10 votes)

Tanner P

a year agoPosted a year ago. Direct link to Tanner P's post “Imaginary numbers are use...”

Imaginary numbers are used a lot in electrical engineering. They can also used to prove a lot of formulas that are useful in real life. And they are useful in any field that uses quadratic equations or polynomials.

When you first learned about negative numbers, they probably seemed weird. How can you have less than nothing? You can’t have -1 apples and you definitely can’t have i apples. But you know now how much math depends on using numbers less than zero, and the same thing goes for imaginary numbers.

(53 votes)

Sarah Myers

8 years agoPosted 8 years ago. Direct link to Sarah Myers's post “Does it matter if the i i...”

Does it matter if the i is in front or behind of the solution.

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(14 votes)

Stefen

8 years agoPosted 8 years ago. Direct link to Stefen's post “As long as it is clear wh...”

As long as it is clear what the i is affecting, you can do both.

EG (2 + 3i) + (4 + 5i) = (2 + 4) + i(3 + 5) or (2 + 4) + (3 + 5)i

However, there are conventions.

When we simplify the above we would normally write 6 + 8i, not 6 + i8, but both are fine, but the second one just looks weird. For example, you are used to the notation "1 + 2", but the following notations "+ 1 2" or "1 2 +" are also acceptable in many situations, through they probably looks weird to you now. (The 1st is Polish Notation, the 2nd Reverse Polish Notation)Another convention is to place the i before the radical, eg i√8. If you want to place it after, make sure to use parenthesis: (√8)i or √8(i), so as to avoid confusion. If you write √8i, do you mean (√8)i or √(8i)?

As you keep studying, you will get more and more exposure to the notation conventions we use.

(38 votes)

KaBoom

a year agoPosted a year ago. Direct link to KaBoom's post “this make no sense”

this make no sense

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(15 votes)

mokracarapacc

a year agoPosted a year ago. Direct link to mokracarapacc's post “simple actually, the key ...”

simple actually, the key here is to understand what "i" means; normally the square root of any negative number is impossible to find, because multiplying 2 same numbers ALWAYS gives a positive result; so we made up a new number called "i" which is just the square root of -1

(16 votes)

kitty-chan

a year agoPosted a year ago. Direct link to kitty-chan's post “Where is I on the number ...”

Where is I on the number line?

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(8 votes)

Tanner P

a year agoPosted a year ago. Direct link to Tanner P's post “Great question! You can't...”

Great question! You can't find i on the number line because it only represents real numbers. So, instead we use the complex

**plane**to represent those numbers. On the complex plane, the real-number axis is horizontal and the imaginary axis is vertical.And the complex plane opens up a lot of interesting ways to look at complex numbers. For example, the complex number 3+4i would be represented by the point (3,4) on the complex plane. So what would the absolute value of 3+4i be? It would be 5, because the distance from the origin (0,0) to (3,4) is 5.

(25 votes)