Find the Domain 3+xi=(x+1)+2i

Problem

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

Solution

1. Identify the equation as an equality of complex numbers, where x is a real variable.

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

3=x+1

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

x=2

4. Equate the imaginary parts of both sides of the equation to verify consistency.

x=2

5. Determine the domain of the variable x based on the context of the problem. Since the task asks for the domain in the context of an equation that simplifies to a single point, and no restrictions are placed on the variable x other than it being a real number in a standard complex equality, the domain of the expression itself (before solving) is all real numbers.

Final Answer

Domain:x∈ℝ

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