Question

(a) $S_1 = \{(x, y, z) \in \mathbb{R}^3 : x = y = z\} \subset \mathbb{R}^3$. (b) $S_2 = \{(x, y, z) \in \mathbb{C}^3 : x = y, y = iz\} \subset \mathbb{C}^3$. (c) $S_3 = \{(x, y, z) \in \mathbb{C}^3 : x = 0\} \subset \mathbb{C}^3$. (d) $S_4 = S_2 \cap S_3 \subset \mathbb{C}^3$. (e) $S_5 = \{(x, y, z) \in \mathbb{C}^3 : x = iz\} \subset \mathbb{C}^3$. (f) $S_6 = S_2 \cap S_5 \subset \mathbb{C}^3$.

          (a) $S_1 = \{(x, y, z) \in \mathbb{R}^3 : x = y = z\} \subset \mathbb{R}^3$.
(b) $S_2 = \{(x, y, z) \in \mathbb{C}^3 : x = y, y = iz\} \subset \mathbb{C}^3$.
(c) $S_3 = \{(x, y, z) \in \mathbb{C}^3 : x = 0\} \subset \mathbb{C}^3$.
(d) $S_4 = S_2 \cap S_3 \subset \mathbb{C}^3$.
(e) $S_5 = \{(x, y, z) \in \mathbb{C}^3 : x = iz\} \subset \mathbb{C}^3$.
(f) $S_6 = S_2 \cap S_5 \subset \mathbb{C}^3$.

$(a) S1 = {(x, y, z) ∈ℝ^3 : x = y = z}⊂ℝ^3. (b) S2 = {(x, y, z) ∈ℂ^3 : x = y, y = iz}⊂ℂ^3. (c) S3 = {(x, y, z) ∈ℂ^3 : x = 0}⊂ℂ^3. (d) S4 = S2 ∩ S3 ⊂ℂ^3. (e) S5 = {(x, y, z) ∈ℂ^3 : x = iz}⊂ℂ^3. (f) S6 = S2 ∩ S5 ⊂ℂ^3.$

Added by Cameron D.

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