What is the value of $$i^{12}$$ ?

$$1$$ (since $$i^{12} = (i^4)^3 = 1^3 = 1$$ ).

$$-i$$ (since $$i^{15} = (i^4)^3 * i^3 = 1^3 * -i = -i$$ ).

What is the value of $$i^{20}$$ ?

$$1$$ (since $$i^{20} = (i^4)^5 = 1^5 = 1$$ ).

Exit Ticket #34 Powers of i Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the value of $i^2$ ?

Back

$-1$

2.

FLASHCARD QUESTION

Front

What is $\sqrt{-64}$ ?

Back

$8i$

3.

FLASHCARD QUESTION

Front

What is $\sqrt{-12}$ ?

Back

$2i\sqrt{3}$

4.

FLASHCARD QUESTION

Front

What is the value of $i^9$ ?

Back

$i$

5.

FLASHCARD QUESTION

Front

What is $\sqrt{-1}$ ?

Back

$i$

6.

FLASHCARD QUESTION

Front

Define the imaginary unit i.

Back

The imaginary unit $i$ is defined as $\sqrt{-1}$ .

7.

FLASHCARD QUESTION

Front

What is the pattern for powers of i?

Back

The powers of $i$ cycle every four: $i^1 = i$ , $i^2 = -1$ , $i^3 = -i$ , $i^4 = 1$ .

8.

FLASHCARD QUESTION

Front

Calculate $i^5$ .

Back

$i$ (since $i^5 = i^4 * i = 1 * i$ ).

9.

FLASHCARD QUESTION

Front

Calculate $i^{10}$ .

Back

$1$ (since $i^{10} = (i^4)^2 * i^2 = 1^2 * -1 = -1$ ).

10.

FLASHCARD QUESTION

Front

What is $\sqrt{-x}$ in terms of i?

Back

$\sqrt{-x} = i\sqrt{x}$ .

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