domain of the complex function 1/z (z is a complex number)

Let's consider the complex number z = x + yi, where x and y are real numbers and i is the imaginary unit. The function is given as:

f(z) = 1/(x + yi)

The domain of the function is the set of all complex numbers for which the function is defined.

The only time the function 1/(x + yi) is not defined is when x + yi = 0. This occurs when both x and y are equal to zero, as division by zero is undefined.

Thus, the domain of the function f(z) = 1/(x + yi) is the set of all complex numbers except for z = 0 (i.e., x ≠ 0 or y ≠ 0). In mathematical notation, this can be represented as:

Domain(f) = {z = x + yi ∈ ℂ | x ≠ 0 or y ≠ 0}

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