Learn about the imaginary unit i, about the imaginary numbers, and about square roots of negative numbers.
what would -i^-i be, would it just be 2^2 • (92 votes) it would be i^3(i^3) = -1^(-1) = 1/-1 = -1 (12 votes) What is the real world application for this?? • (62 votes) 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, (180 votes) the brain can not blow up unless it was overloaded with knowlege (32 votes) hard to believe there are people out there that imagine numbers • (33 votes) 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. (30 votes) 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? • (20 votes) 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. (34 votes) 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? • (9 votes) 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. (44 votes) 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? • (5 votes) 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 Now we have this concept of "the complex numbers" that we can further explore. Application to reality is not necessary. (48 votes) Does it matter if the i is in front or behind of the solution. • (11 votes) As long as it is clear what the i is affecting, you can do both. 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. (32 votes) this make no sense • (12 votes) 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 (12 votes) Where is I on the number line? • (7 votes) 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. (22 votes)Want to join the conversation?
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.
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)
