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

$$\sqrt{-x} = i\sqrt{x}$$ for any positive real number $$x$$ .

What is the value of $$i^5$$ ?

$$i^5 = i^4 * i = 1 * i = i$$ .

How do you express $$i^7$$ in simplest form?

$$i^7 = i^4 * i^3 = 1 * (-i) = -i$$ .

What is the value of $$i^{10}$$ ?

$$i^{10} = i^8 * i^2 = 1 * (-1) = -1$$ .

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

$$i^{12} = i^{8} * i^{4} = 1 * 1 = 1$$ .

Imaginary Numbers / Powers of i Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the value of $i^3$ ?

Back

$-i$

2.

FLASHCARD QUESTION

Front

What is the value of $12i^2$ ?

Back

$-12$

3.

FLASHCARD QUESTION

Front

What is $\sqrt{-12}$ expressed in terms of i?

Back

$2i\sqrt{3}$

4.

FLASHCARD QUESTION

Front

What is the value of $i^2$ ?

Back

$-1$

5.

FLASHCARD QUESTION

Front

What is the value of $i^6$ ?

Back

$-1$

6.

FLASHCARD QUESTION

Front

Define imaginary numbers.

Back

Imaginary numbers are numbers that can be written as a real number multiplied by the imaginary unit $i$ , where $i = \sqrt{-1}$ .

7.

FLASHCARD QUESTION

Front

What is the imaginary unit $i$ ?

Back

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

8.

FLASHCARD QUESTION

Front

What is the relationship between $i^2$ and real numbers?

Back

$i^2 = -1$ , which shows that imaginary numbers are related to negative values.

9.

FLASHCARD QUESTION

Front

How do you simplify $i^4$ ?

Back

$i^4 = (i^2)^2 = (-1)^2 = 1$ .

10.

FLASHCARD QUESTION

Front

What is the pattern in the powers of $i$ ?

Back

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

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