Find the Domain

Problem

z=7*(cos(15^∘)+i*sin(15^∘))⋅(2*(cos(110^∘)+i*sin(110^∘)))

Solution

1. Identify the nature of the expression. The task asks for the "Domain" of a complex number multiplication, but in the context of complex numbers, this usually refers to the set of possible input values for a function. Since z is a constant expression with no variables, the expression is defined for all real values of the arguments provided.

2. Recognize that the expression is a product of two complex numbers in polar form, (z_1)=(r_1)*(cos((θ_1))+i*sin((θ_1))) and (z_2)=(r_2)*(cos((θ_2))+i*sin((θ_2)))

3. Determine if there are any restrictions. The functions cos(θ) and sin(θ) are defined for all real numbers θ

4. Conclude that since there are no variables, square roots of negative numbers (in a real context), or denominators that could be zero, the expression is a well-defined constant. If the task implies finding the domain of a constant function ƒ(x)=z the domain is all real numbers. However, for a static complex value, the "domain" is not a standard property; if interpreted as the set of valid inputs for the trigonometric components, it is all real numbers.

Final Answer

Domain=(−∞,∞)

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