which of the following is an example of a complex number that is not in the set of real numbers?

-7
(2 + \sqrt{3})
(4 + 9i)
(\pi)

Question

which of the following is an example of a complex number that is not in the set of real numbers?

-7
(2 + \sqrt{3})
(4 + 9i)
(\pi)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Complex Numbers", "Real Numbers", "Imaginary Numbers" ], "current_concepts": [ "Complex Numbers", "Real Numbers", "Imaginary Numbers" ] } ## Define real and non-real complex numbers $$ \begin{aligned} &\mathbb{C} = \{a + bi \mid a, b \in \mathbb{R}, i^2 = -1\} \ &\mathbb{R} = \{a + bi \in \mathbb{C} \mid b = 0\} \ &\mathbb{C} \setminus \mathbb{R} = \{a + bi \in \mathbb{C} \mid b eq 0\} \end{aligned} $$ ## Evaluate the given options $$ \begin{aligned} &-7 \implies b = 0 \implies -7 \in \mathbb{R} \ &2 + \sqrt{3} \implies b = 0 \implies 2 + \sqrt{3} \in \mathbb{R} \ &4 + 9i \implies b = 9 eq 0 \implies 4 + 9i otin \mathbb{R} \ &\pi \implies b = 0 \implies \pi \in \mathbb{R} \end{aligned} $$ ## Identify the non-real complex number $$ 4 + 9i \in \mathbb{C} \setminus \mathbb{R} $$

(A) $-7$

(B) $2 + \sqrt{3}$

(C) $4 + 9i$

(D) $\pi$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Complex Numbers" ] }

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QUESTION IMAGE

Question

Explanation:

Define real and non-real complex numbers

Evaluate the given options

Identify the non-real complex number

Answer: