drag the tiles to the correct boxes to complete the pairs.
match each power of i to its equivalent expression.

pairs
$i^{81}$ $\longrightarrow$
$i^{52}$ $\longrightarrow$
$i^{99}$ $\longrightarrow$
$i^{66}$ $\longrightarrow$

tiles
1, -1, i, -i

Question

drag the tiles to the correct boxes to complete the pairs.
match each power of i to its equivalent expression.

pairs
$i^{81}$ $\longrightarrow$
$i^{52}$ $\longrightarrow$
$i^{99}$ $\longrightarrow$
$i^{66}$ $\longrightarrow$

tiles
1, -1, i, -i

Accepted Answer

{ "quality": "clear", "question_count": 4, "skills_matched": [ "step_cot", "table_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Powers of i", "Imaginary Unit Powers" ], "new_concepts": [], "current_concepts": [ "Powers of i", "Imaginary Unit Powers" ] } ## Simplify each power of $i$ using division by 4 $$ \begin{aligned} &i^{81} = i^{4 \times 20 + 1} = (i^4)^{20} \cdot i^1 = 1^{20} \cdot i = i\ &i^{52} = i^{4 \times 13} = (i^4)^{13} = 1^{13} = 1\ &i^{99} = i^{4 \times 24 + 3} = (i^4)^{24} \cdot i^3 = 1^{24} \cdot (-i) = -i\ &i^{66} = i^{4 \times 16 + 2} = (i^4)^{16} \cdot i^2 = 1^{16} \cdot (-1) = -1 \end{aligned} $$ | No. | Problem | Answer | |---|---|---| | 1 | $i^{81}$ | $i$ | | 2 | $i^{52}$ | $1$ | | 3 | $i^{99}$ | $-i$ | | 4 | $i^{66}$ | $-1$ | { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Powers of i" ] }

No.	Problem	Answer
2	\(i^{52}\)	\(1\)
3	\(i^{99}\)	\(-i\)
4	\(i^{66}\)	\(-1\)

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Simplify each power of \(i\) using division by 4

Answer: