question 2
drag each label to the correct location on the chart.
classify the expressions based on whether they represent purely real numbers or non-real complex numbers.

purely real number | non-real complex number

$\sqrt{(-5)^2}$
$400$
$-9 + 10i^2$
$0 + 5i$
$i^8$
$\sqrt{-16}$
$-2 + 6i$
$\sqrt{-10}$

Question

question 2
drag each label to the correct location on the chart.
classify the expressions based on whether they represent purely real numbers or non-real complex numbers.

purely real number | non-real complex number

$\sqrt{(-5)^2}$
$400$
$-9 + 10i^2$
$0 + 5i$
$i^8$
$\sqrt{-16}$
$-2 + 6i$
$\sqrt{-10}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Number Classification", "Real Number Subsets", "Powers of i", "Complex Numbers" ], "new_concepts": [], "current_concepts": [ "Number Classification", "Real Number Subsets", "Powers of i", "Complex Numbers" ] } ## Evaluate each expression $$ \begin{aligned} &\sqrt{(-5)^2} = \sqrt{25} = 5 \quad (\text{Real}) \ &400 \quad (\text{Real}) \ &-9 + 10i^2 = -9 + 10(-1) = -19 \quad (\text{Real}) \ &0 + 5i = 5i \quad (\text{Non-real Complex}) \ &i^8 = (i^4)^2 = 1^2 = 1 \quad (\text{Real}) \ &\sqrt{-16} = 4i \quad (\text{Non-real Complex}) \ &-2 + 6i \quad (\text{Non-real Complex}) \ &\sqrt{-10} = i\sqrt{10} \quad (\text{Non-real Complex}) \end{aligned} $$ ## Group the expressions $$ \begin{aligned} &\text{Purely Real Number:} \quad \sqrt{(-5)^2}, \ 400, \ -9 + 10i^2, \ i^8 \ &\text{Non-real Complex Number:} \quad 0 + 5i, \ \sqrt{-16}, \ -2 + 6i, \ \sqrt{-10} \end{aligned} $$ | Purely Real Number | Non-real Complex Number | | :--- | :--- | | $\sqrt{(-5)^2}$ | $0 + 5i$ | | $400$ | $\sqrt{-16}$ | | $-9 + 10i^2$ | $-2 + 6i$ | | $i^8$ | $\sqrt{-10}$ | { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Complex Numbers" ] }

Purely Real Number	Non-real Complex Number
\(400\)	\(\sqrt{-16}\)
\(-9 + 10i^2\)	\(-2 + 6i\)
\(i^8\)	\(\sqrt{-10}\)

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Evaluate each expression

Group the expressions

Answer: