No inductor is perfect and has a capacitive and resistive component. As frequency increases, these components have more effect on the circuit operation. A capacitive component would be out of phase and be the imaginary value.
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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.
The imaginary part is expressed as a product of i(square root of negative one), typically following a plus sign, so that the complex number has the form a + bi, with "a" the real part and "bi" the imaginary part.
A complex number has a real part and a (purely) imaginary part, So imaginary numbers are a subset of complex numbers. But the converse is not true. A real number is also a member of the complex domain but it is not an imaginary number.
Square roots of negative numbers are complex, meaning that they carry a 'real' and an 'imaginary' part. Here the real part is approximately 5.8309518948453 and the imaginary part is i.
A complex number comes in two parts: a real part and an imaginary part. If the value of the real part is a and the value of the imaginary part is b, the number is written as a + bi.