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The letter i represents the imaginary unit [square root of -1]. It's added after the number. So 5i means 5 units in the positive imaginary direction, or just 5 times sqrt(-1).
In electrical engineering, often the letter j is used, because i represents current in electrical notation.
CommentIn electrical engineering, the operator 'j' is usually placed in front of a number, not behind it: i.e. (a+jb) not (a +bj).
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Can a number be imaginary but not pure imaginary?
Yes. The number 1 + i is imaginary but not pure imaginary, while 5i is pure imaginary.
Is the difference of a complex number and its conjugate a real imaginary or pure imaginary number?
It is a pure imaginary number.Since (a+bi)-(a-bi) = 2bi, it is a pure imaginary number (it has no real component).
Is -23 an imaginary number?
No, but √-23 is. An imaginary number is the square root of a negative number.
Are imaginary and complex numbers the same?
No. A complex number is a number that has both a real part and an imaginary part. Technically, a pure imaginary number ... which has no real part ... is not a complex number.
Is the square root of negative two an irrational number?
No, it is an imaginary number which is a complex number.
