what is the value of $i^{20+1}$?

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$\bigcirc$ -1
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Question

what is the value of $i^{20+1}$?

$\bigcirc$ 1
$\bigcirc$ -1
$\bigcirc$ -i
$\bigcirc$ i

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": [ "Powers of i", "Imaginary Unit Cycle" ], "current_concepts": [ "Imaginary Numbers", "Powers of i", "Exponent Rules" ] } ## Simplify the exponent $$ i^{20+1} = i^{21} $$ ## Apply the cyclic property of powers of i $$ i^{21} = i^{20} \cdot i^1 = (i^4)^5 \cdot i $$ ## Evaluate the expression $$ (1)^5 \cdot i = i $$

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i

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

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QUESTION IMAGE

Question

Explanation:

Simplify the exponent

Apply the cyclic property of powers of i

Evaluate the expression

Answer: