What is the value of $$i^{60}$$ ?

$$i^{60} = i^{(60 \\mod 4)} = i^0 = 1$$ .

What is the value of $$i^{48}$$ ?

$$i^{48} = i^{(48 \\mod 4)} = i^0 = 1$$ .

How do you simplify $$-9i^{43}$$ ?

$$-9i^{43} = -9i^{(43 \\mod 4)} = -9i^3 = 9i$$ .

What is the imaginary unit i?

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

What is the result of $$(-2i)(3i)(-5i^{48})$$ ?

$$(-2i)(3i)(-5i^{48}) = -30i$$ .

Imaginary numbers and powers of i Flashcards

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15 questions

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1.

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 is defined as $i = \sqrt{-1}$ .

Tags

CCSS.HSN.CN.A.1

2.

FLASHCARD QUESTION

Front

What is the value of i raised to the power of 1?

Back

$i^1 = i$ .

Tags

CCSS.HSN.CN.A.1

3.

FLASHCARD QUESTION

Front

What is the value of i raised to the power of 2?

Back

$i^2 = -1$ .

Tags

CCSS.HSN.CN.A.1

4.

FLASHCARD QUESTION

Front

What is the value of i raised to the power of 3?

Back

$i^3 = -i$ .

Tags

CCSS.HSN.CN.A.2

5.

FLASHCARD QUESTION

Front

What is the value of i raised to the power of 4?

Back

$i^4 = 1$ .

Tags

CCSS.HSN.CN.A.2

6.

FLASHCARD QUESTION

Front

What is the pattern in the powers of i?

Back

The powers of i repeat every four terms: $i, -1, -i, 1$ .

Tags

CCSS.HSN.CN.A.2

7.

FLASHCARD QUESTION

Front

How do you simplify $i^{61}$ ?

Back

$i^{61} = i^{(61 \mod 4)} = i^1 = i$ .

Tags

CCSS.HSN.CN.A.2

8.

FLASHCARD QUESTION

Front

What is the result of multiplying two imaginary numbers, such as $(-2i)(3i)$ ?

Back

$(-2i)(3i) = -6i^2 = 6$ .

Tags

CCSS.HSN.CN.A.2

9.

FLASHCARD QUESTION

Front

How do you add complex numbers, such as $(12 - 4i) + (-2 + 8i)$ ?

Back

Combine real parts and imaginary parts: $(12 - 2) + (-4i + 8i) = 10 + 4i$ .

Tags

CCSS.HSN.CN.A.2

10.

FLASHCARD QUESTION

Front

What is the value of $i^{19}$ ?

Back

$i^{19} = i^{(19 \mod 4)} = i^3 = -i$ .

Tags

CCSS.HSN.CN.A.2

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