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even if you can't see it.... the number is real. but question to that, what's the number?
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Clearly, the above answer was provided by someone who had no knowledge of the complex field.
A real number cannot be a pure imaginary number, nor can it contain any part that is imaginary.
In the context of the coordinate plane, the real numbers can be seen as the x-axis, the pure imaginary numbers form the y-axis excluding the origin. Complex numbers are all the point in the four quadrants.
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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).
Can a complex number can't be a pure imaginary number?
A complex number can be a pure imaginary, or a pure real number, or a combination of the two. The form for a complex number is a + bi, where a & b can be any real numbers (so if a = 0, then the number is pure imaginary; and if b=0, then it is a real 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 every complex number a pure imaginary number?
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.
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.
