select the correct answer from each drop-down menu.

simplify the expressions.

$i^{32} =$ choose an answer

$i^{25} =$ choose an answer

$i^{86} =$ choose an answer

$i^{51} =$ choose an answer

Question

select the correct answer from each drop-down menu.

simplify the expressions.

$i^{32} =$ choose an answer

$i^{25} =$ choose an answer

$i^{86} =$ choose an answer

$i^{51} =$ choose an answer

Accepted Answer

{ "quality": "clear", "question_count": 4, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Exponent Rules" ], "new_concepts": [ "Powers of i", "Imaginary Unit Powers" ], "current_concepts": [ "Exponent Rules", "Powers of i", "Imaginary Unit Powers" ] } ## Determine powers of the imaginary unit $i$ $$ \begin{aligned} i^1 &= i \ i^2 &= -1 \ i^3 &= -i \ i^4 &= 1 \end{aligned} $$ ## Simplify each expression using division by 4 $$ \begin{aligned} 32 \div 4 &= 8 \text{ R } 0 \implies i^{32} = i^0 = 1 \ 25 \div 4 &= 6 \text{ R } 1 \implies i^{25} = i^1 = i \ 86 \div 4 &= 21 \text{ R } 2 \implies i^{86} = i^2 = -1 \ 51 \div 4 &= 12 \text{ R } 3 \implies i^{51} = i^3 = -i \end{aligned} $$ ## Question 1 $i^{32} =$ 1 ## Question 2 $i^{25} =$ $i$ ## Question 3 $i^{86} =$ -1 ## Question 4 $i^{51} =$ $-i$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Powers of i" ] }

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QUESTION IMAGE

Question

Explanation:

Determine powers of the imaginary unit \(i\)

Simplify each expression using division by 4

Answer:

Question 1

Question 2

Question 3

Question 4