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A $$d$$-dimensional real vector $$\mathbf{x} = (x_1, x_2, \dots, x_d)$$ can be reinterpreted as a $$d/2$$-dimensional complex vector $$\mathbf{x}'$$ by pairing consecutive real components into the real and imaginary parts of each new complex component: $$\mathbf{x}' = (x'_1, x'_2, \dots, x'_{d/2}) = (x_1 + i x_2,\ x_3 + i x_4,\ \dots,\ x_{d-1} + i x_d),$$ where $$i$$ is the imaginary unit. This reinterpretation requires $$d$$ to be even.

Complex Vector Representation from Paired Real Components

A 2-dimensional complex vector $\mathbf{c} = (5 - 2i, -1 + 8i)$ was created by reinterpreting a 4-dimensional real vector $\mathbf{r}$ by pairing consecutive real components to form the real and imaginary parts of each complex component. What is the original real vector $\mathbf{r}$? Please write your answer as a sequence of numbers in parentheses, separated by commas.

Reconstructing a Real Vector from its Complex Representation

A 7-dimensional real vector can be reinterpreted as a 3.5-dimensional complex vector by pairing its consecutive real components to form the real and imaginary parts of new complex components.

A 6-dimensional real vector is given by $\mathbf{v} = (2, -5, 0, 1, 8, 3)$. If this vector is reinterpreted as a 3-dimensional complex vector by pairing consecutive components (where the first component of a pair is the real part and the second is the imaginary part), what is the resulting complex vector?

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