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An imaginary number is the product of a real number and the imaginary unit i, which is defined by its property i 2 = −1. The square of an imaginary number bi is −b 2. For example, 5i is an imaginary number, and its square is −25. The number zero is considered to be both real and imaginary.
Learn about the imaginary unit i, the square roots of negative numbers, and how they solve some quadratic equations. See examples, definitions, properties, and simplification methods of imaginary numbers.
- what would -i^-i be, would it just be 2^2it would be i^3(i^3) = -1^(-1) = 1/-1 = -1
- What is the real world application for this??design, simulation, analysis of normal and semiconductor circuits, acoustics and speakers, physics., mechanical system vibration, automotive exhaus...
- my brain blew upthe brain can not blow up unless it was overloaded with knowlege
- hard to believe there are people out there that imagine numbersTechnically, numbers and mathematics in general are all imaginary. Mathematics is not a physical object that literally exists in the seeable univer...
- Can you have different answers to simplifying depending on what numbers you take from the original, ...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.
- this make no sensesimple actually, the key here is to understand what "i" means; normally the square root of any negative number is impossible to find, because multi...
- Does it matter if the i is in front or behind of the solution.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 a...
- How would one use an imaginary number in real life? If it is imaginary, would it have any use cases?...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 ar...
- Where is I on the number line?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 th...
- If imaginary numbers aren't real, how is it possible to use them in real life? You can't count thing...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...
Imaginary numbers are numbers that have a negative square root, such as i or j. They are useful for solving equations, making complex numbers, and describing sounds and currents. Learn how to identify, create, and use them with examples, formulas, and applications.
Learn what imaginary numbers are, how to perform arithmetic operations on them, and how to find their conjugate pairs. Imaginary numbers are the square root of negative numbers, written as real numbers multiplied by the imaginary unit i.
- 8 min
Learn what imaginary numbers are, how they relate to negative numbers, and why they are useful in math and physics. See diagrams, examples, and analogies to understand the concept of i and complex numbers.
- 14 min
Learn what imaginary numbers are, how they are used in complex numbers and Fourier transforms, and how to calculate their powers. See examples of imaginary numbers and their squares, and how they relate to real numbers.
Learn about the imaginary unit, "i", a unique number defined as the square root of -1. It's a key part of complex numbers, which are in the form a + bi. See examples, questions, and comments on this topic.
- 5 min
- Sal Khan
