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Jan 2, 2024 · Definition of Imaginary Numbers. Imaginary numbers are numbers that can be written as a real number multiplied by the imaginary unit i, which is defined by the property i²=−1. Simply put, the square root of -1 is termed as ‘i’. So, if we talk about the square root of -4, it’s represented as i².
- Using I
- Unit Imaginary Number
- Imaginary Numbers Are Not "Imaginary"
- Imaginary Numbers Are Useful
- Interesting Property
- Conclusion
Interesting! We used an imaginary number (5i) and ended up with a real solution (−25). Imaginary numbers can help us solve some equations: Can you take the square root of −1? Well ican!
The square root of minus one √(−1) is the "unit" Imaginary Number, the equivalent of 1for Real Numbers. In mathematics the symbol for √(−1) is ifor imaginary. But in electronics the symbol is j, because iis used for current, and j is next in the alphabet.
Imaginary Numbers were once thought to be impossible, and so they were called "Imaginary" (to make fun of them). But then people researched them more and discovered they were actually useful and importantbecause they filled a gap in mathematics ... but the "imaginary" name has stuck. And that is also how the name "Real Numbers" came about (real is ...
Complex Numbers
Imaginary numbers become most useful when combined with real numbers to make complex numbers like 3+5i or 6−4i
Spectrum Analyzer
Those cool displays you see when music is playing? Yep, Complex Numbers are used to calculate them! Using something called "Fourier Transforms". In fact many clever things can be done with sound using Complex Numbers, like filtering out sounds, hearing whispers in a crowd and so on. It is part of a subject called "Signal Processing".
Electricity
AC (Alternating Current) Electricity changes between positive and negative in a sine wave. When we combine two AC currents they may not match properly, and it can be very hardto figure out the new current. But using complex numbers makes it a lot easier to do the calculations. And the result may have "Imaginary" current, but it can still hurt you!
The Unit Imaginary Number, i, has an interesting property. It "cycles" through 4 different values each time we multiply: So we have this:
The unit imaginary number, i, equals the square root of minus 1 Imaginary Numbers are not "imaginary", they really exist and have many uses.
This worksheet is designed to provide lots of problems in the “I think of a number” format. Learners could be encouraged to try working backwards to solve them where possible, using a function machine or, ideally form an equation.
Jun 28, 2022 · The Corbettmaths practice questions on Think of a Number style questions.
Sep 2, 2019 · The Corbettmaths Practice Questions on Multiples, Factors and Primes.
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