simplify.

$(-i)^{66}$

$(-i)^{66} = $

(simplify your answer. type your answer in the form a + bi.)

Question

simplify.

$(-i)^{66}$

$(-i)^{66} = $

(simplify your answer. type your answer in the form a + bi.)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Imaginary Numbers" ], "new_concepts": [ "Powers of i" ], "current_concepts": [ "Imaginary Numbers", "Powers of i" ] } ## Distribute the exponent $$ (-i)^{66} = (-1)^{66} \cdot i^{66} $$ ## Evaluate the negative base power $$ (-1)^{66} = 1 $$ ## Simplify the power of i $$ \begin{aligned} i^{66} &= i^{64 + 2} \ &= (i^4)^{16} \cdot i^2 \ &= (1)^{16} \cdot (-1) \ &= -1 \end{aligned} $$ Thus, the expression simplifies to $-1$. Written in the form $a + bi$, it is $-1 + 0i$. $(-i)^{66} =$ $-1 + 0i$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Powers of i" ] }

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QUESTION IMAGE

Question

Explanation:

Distribute the exponent

Evaluate the negative base power

Simplify the power of i

Answer: