Find the Domain z=1+ square root of 3i

Problem

z=1+√(,3*i)

Solution

1. Identify the nature of the expression. The task asks for the "Domain" of a constant complex number z

2. Analyze the components. The expression z=1+√(,3*i) consists of fixed numerical values and the imaginary unit i

3. Determine the domain. In mathematics, the domain refers to the set of possible input values for which a function is defined. Since z is a constant value and not a function of a variable (like x, it does not have a domain in the traditional sense.

4. Interpret the context. If the expression is viewed as a constant function ƒ(w)=1+√(,3*i) the domain is the set of all complex numbers ℂ However, as a standalone complex number, the concept of a domain does not apply.

5. Evaluate the square root of the imaginary part if simplification is required. Using the formula for the square root of a complex number a+b*i

√(,3*i)=√(,3)⋅√(,i)

√(,i)=1/√(,2)+i/√(,2)

√(,3*i)=√(,3/2)+i√(,3/2)

Final Answer

z=1+√(,3/2)+i√(,3/2)

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