What is the relationship between imaginary numbers and complex numbers?

Imaginary numbers are a subset of complex numbers, which are expressed in the form $$a + bi$$ , where $$a$$ is the real part and $$b$$ is the imaginary part.

Imaginary Numbers / Powers of i Flashcards

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16 questions

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1.

FLASHCARD QUESTION

Front

What is the value of $i^6$ ?

Back

-1

2.

FLASHCARD QUESTION

Front

Simplify $\sqrt{-12}$ .

Back

$2i\sqrt{3}$

3.

FLASHCARD QUESTION

Front

What is the value of $i^3$ ?

Back

$-i$

4.

FLASHCARD QUESTION

Front

Simplify $\sqrt{-1}$ .

Back

i

5.

FLASHCARD QUESTION

Front

Simplify $\sqrt{-4}$ .

Back

$2i$

6.

FLASHCARD QUESTION

Front

What is the definition of an imaginary number?

Back

An imaginary number is a number 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 value of $i^2$ ?

Back

-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 $i^0$ ?

Back

1

10.

FLASHCARD QUESTION

Front

How do you express $\sqrt{-x}$ in terms of $i$ ?

Back

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

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