How do you simplify $$\sqrt{-x}$$ ?

$$\sqrt{-x} = i\sqrt{x}$$ for x > 0

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

$$-1$$ (follows the pattern of powers of i)

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

$$1$$ (follows the pattern of powers of i)

What is the relationship between complex numbers and the Cartesian plane?

$$Complex numbers can be represented as points in the Cartesian plane, where the x-axis is the real part and the y-axis is the imaginary part.$$

Exploring Powers of i and Roots Flashcards: 15 Cards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the value of $i^8$ ?

Back

$1$

2.

FLASHCARD QUESTION

Front

What is the value of $i^3$ ?

Back

$-i$

3.

FLASHCARD QUESTION

Front

Simplify $\sqrt{-16}$ .

Back

$4i$

4.

FLASHCARD QUESTION

Front

What is the value of $i^6$ ?

Back

$-1$

5.

FLASHCARD QUESTION

Front

Simplify $\sqrt{-9}$ .

Back

$3i$

6.

FLASHCARD QUESTION

Front

What is the definition of the imaginary unit $i$ ?

Back

$i = \sqrt{-1}$

7.

FLASHCARD QUESTION

Front

What is the pattern of powers of $i$ ?

Back

$i^1 = i, i^2 = -1, i^3 = -i, i^4 = 1 (repeats every 4 powers)$

8.

FLASHCARD QUESTION

Front

What is $i^0$ equal to?

Back

$1$ (Any non-zero number raised to the power of 0 is 1)

9.

FLASHCARD QUESTION

Front

What is the value of $i^5$ ?

Back

$i$ (follows the pattern of powers of i)

10.

FLASHCARD QUESTION

Front

What is the value of $i^7$ ?

Back

$-i$ (follows the pattern of powers of i)

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