Find the Domain 2+xi=(x+1)+i

Problem

2+x*i=(x+1)+i

Solution

1. Identify the nature of the equation, which involves complex numbers where i is the imaginary unit.

2. Equate the real parts of both sides of the equation to find the value of x

2=x+1

3. Solve for x by subtracting 1 from both sides.

x=1

4. Verify the imaginary parts by substituting x=1 into the coefficients of i

x*i=i

1*i=i

5. Determine the domain of the variable x Since the equation is a linear equality that holds true for a specific value, and there are no square roots of negative variables, denominators containing variables, or logarithms, x can theoretically be any real number in the context of the expressions used. However, the "domain" in the context of a single variable equation usually refers to the set of all possible input values for which the equation is defined.

6. Conclude that the expressions 2+x*i and (x+1)+i are polynomials with respect to x which are defined for all real numbers.

Final Answer

Domain:(−∞,∞)

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