What is the value of $$i^{123}$$ ?

$$i^{123} = -i$$ (since 123 mod 4 = 3).

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

$$i^{8} = 1$$ (since 8 mod 4 = 0).

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

$$i^{12} = 1$$ (since 12 mod 4 = 0).

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

$$i^{5} = i$$ (since 5 mod 4 = 1).

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1.

FLASHCARD QUESTION

Front

What is the value of $i^{44}$ ?

Back

1

2.

FLASHCARD QUESTION

Front

What is the value of $i^{61}$ ?

Back

$i$

3.

FLASHCARD QUESTION

Front

What is the value of $i^{26}$ ?

Back

-1

4.

FLASHCARD QUESTION

Front

What is the value of $i^{1522}$ ?

Back

-1

5.

FLASHCARD QUESTION

Front

What is the value of $i^{322}$ ?

Back

-1

6.

FLASHCARD QUESTION

Front

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

Back

The imaginary unit 'i' is defined as $i = \frac{\text{sqrt}(-1)}{1}$ .

7.

FLASHCARD QUESTION

Front

What is the pattern of powers of 'i'?

Back

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

8.

FLASHCARD QUESTION

Front

How do you determine the value of $i^n$ for any integer n?

Back

To find $i^n$ , divide n by 4 and use the remainder to determine the value based on the cycle.

9.

FLASHCARD QUESTION

Front

What is $i^0$ ?

Back

$i^0 = 1$ for any non-zero number.

10.

FLASHCARD QUESTION

Front

What is the value of $i^{100}$ ?

Back

$i^{100} = 1$ (since 100 mod 4 = 0).

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