if someone has an imaginary friend then that is an example or if the brain tricks you into seeing someting that isn't there then its using imaginary effects on you
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No. For example the number 1+i. Pure imaginary complex numbers are of the form 0 + a*i, where a is a non-zero real number.
The only thing I can think of that you might mean is an imaginary or complex number. Since there is no solution to √(-1) mathematicians labeled it as i which is the imaginary number, and any number that includes purely i is also imaginary. Complex numbers are a mix of both real and imaginary numbers. for example 3 is real, 5i is imaginary and 3+5i is complex. Hopefully this answers what you meant.
No. The square root of negative one is an example of an imaginary (not real) number. Pi is irrational, but real.
Imaginary number is a number that consist of only Imaginary part. Such as i, 40i, 1/2i, etc. While the difference between the imaginary numbers and the complex numbers are that complex number also contains Real numbers, and can be written as a + bi. For example, 30+i, 1/2+1/2i, etc.
Yes. The number 1 + i is imaginary but not pure imaginary, while 5i is pure imaginary.