Find the Domain (x^3-3ix-5(1+i))÷(x-1+i)

Problem

Domain of (x3−3*i*x−5*(1+i))/(x−1+i)

Solution

1. Identify the type of function. This is a rational function, which is defined for all complex numbers except where the denominator is equal to zero.

2. Set the denominator equal to zero to find the excluded value of x

x−1+i=0

3. Solve for x by isolating the variable on one side of the equation.

x=1−i

4. State the domain as all complex numbers except for the value that makes the denominator zero.

Final Answer

Domain={[x∈ℂ,x≠1−i]}

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