if $i = \sqrt{-1}$, what is the value of $i^3$?

-1
$i$
1
$-i$

Question

if $i = \sqrt{-1}$, what is the value of $i^3$?

-1
$i$
1
$-i$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Imaginary Numbers" ], "new_concepts": [ "Powers of i" ], "current_concepts": [ "Imaginary Numbers", "Powers of i" ] } ## Define the imaginary unit and its square $$ \begin{aligned} i &= \sqrt{-1} \ i^2 &= -1 \end{aligned} $$ ## Express the cubic power in terms of lower powers $$ i^3 = i^2 \cdot i $$ ## Substitute the value of the square and simplify $$ i^3 = (-1) \cdot i = -i $$

-1

i

1

-i

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

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QUESTION IMAGE

Question

Explanation:

Define the imaginary unit and its square

Express the cubic power in terms of lower powers

Substitute the value of the square and simplify

Answer: