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Adjoint operator of a complex number?
The absolute value of a complex number is the magnitude of the number, which is found from sqrt(a² + b²) for the complex number a + bi
Yes. And since Real numbers are a subset of complex numbers, a complex number can also be a pure real.
Yes, for example: (0 + j5) is a complex number, whose 'real' number is zero.
You get a complex number unless the real number happens to be 0 or 1.