what is the value of $i^{97} - i$?

- $-i$
- $0$
- $-2i$
- $i^{96}$

Question

what is the value of $i^{97} - i$?

- $-i$
- $0$
- $-2i$
- $i^{96}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Powers of i", "Complex Number Subtraction" ], "new_concepts": [], "current_concepts": [ "Powers of i", "Complex Number Subtraction" ] } ## Simplify the power of i $$ \begin{aligned} 97 &= 4 \times 24 + 1 \ i^{97} &= i^{4 \times 24 + 1} = (i^4)^{24} \times i^1 = 1^{24} \times i = i \end{aligned} $$ ## Evaluate the expression $$ i^{97} - i = i - i = 0 $$

-i

0

-2i

i^{96}

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Powers of i" ] }

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Question

Explanation:

Simplify the power of i

Evaluate the expression

Answer: