What is the value of $$i^8$$ ?

$$1$$ (since $$i^8 = (i^4)(i^4) = 1 * 1$$ ).

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

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

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

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

What is the value of $$i^{14}$$ ?

$$-i$$ (since $$i^{14} = (i^4)^3 * i^2 = 1 * -1$$ ).

Explain the significance of imaginary numbers in mathematics.

Imaginary numbers extend the real number system, allowing for solutions to equations like $$x^2 + 1 = 0$$ , which have no real solutions.

Imaginary Numbers Flashcards

Student preview

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 the value of $i^3$ ?

Back

$-i$

3.

FLASHCARD QUESTION

Front

What is the value of $i^{13}$ ?

Back

$i$

4.

FLASHCARD QUESTION

Front

What is the value of $i^5$ ?

Back

$i$

5.

FLASHCARD QUESTION

Front

What is the value of $i^4$ ?

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 $i = \sqrt{-1}$ .

8.

FLASHCARD QUESTION

Front

What is the pattern of powers of $i$ ?

Back

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

9.

FLASHCARD QUESTION

Front

What is the value of $i^6$ ?

Back

$-1$ (since $i^6 = (i^4)(i^2) = 1 * -1$ ).

10.

FLASHCARD QUESTION

Front

What is the value of $i^7$ ?

Back

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

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