Question 1

Which of the following is the value of $$i^{67}$$?

Accepted Answer

$$-i$$

Question 2

If $$i = \sqrt{-1}$$, what is $$i^{1003}$$ simplified?

Accepted Answer

$$i$$

Question 3

A medical imaging device uses the value $$i^{222} in $$its calculations. What is the simplified value?

Accepted Answer

$$1$$

Question 4

Which of the following is true about the powers of $$i$$?

Accepted Answer

They repeat every 4 powers.

Question 5

A chemist encounters $$i^{85} in a $$calculation. What is its simplified value?

Accepted Answer

$$-i$$

Question 6

Which of the following is the correct sequence for the first four powers of $$i$$?

Accepted Answer

Question 7

A student is asked to simplify $$i^{100}. $$What is the result?

Accepted Answer

$$1$$

Question 8

Which shortcut can be used to evaluate $$i^n$$ for large $$n$$?

Accepted Answer

Divide $$n by 4 $$and use the remainder.

Question 9

If $$i^{4k} = 1$ for any integer k$, what is i$$^{400}$$?

Accepted Answer

$$1$$

Question 10

A physicist uses $$i^{1002} in a $$calculation. What is its simplified value?

Accepted Answer

$$-1$$

Question 11

Which of the following is NOT a possible value for $$i^n$$?

Accepted Answer

$$2$$

Question 12

If $$i^{n} is $$simplified and $$n$$ leaves a remainder of 2 when divided by 4, what is the value?

Accepted Answer

$$-1$$

Question 13

A computer engineer needs to simplify $$i^{2023}. $$What is the result?

Accepted Answer

$$i$$

Question 14

Which of the following statements is correct about $$i^{n}$$?

Accepted Answer

For any integer $$n$$, $$i^{n}$$ can be $$i$$, $$-i$$, $$1$$, or $$-1.$$

Question 15

If $$i^{n} is $$simplified and $$n$$ leaves a remainder of 3 when divided by 4, what is the value?

Accepted Answer

$$-i$$

Question 16

A biologist calculates $$i^{0} in a $$formula. What is the value?

Accepted Answer

$$1$$

Question 17

Which of the following is the value of $$i^{25}$$?

Accepted Answer

$$i$$

Question 18

A student is asked to simplify $$i^{2222}. $$What is the result?

Accepted Answer

$$1$$

Question 19

If $$i^{n} is $$simplified and $$n$$ leaves a remainder of 1 when divided by 4, what is the value?

Accepted Answer

$$i$$

Question 20

Which of the following is the value of $$i^{1001}$$?

Accepted Answer

$$-i$$

Powers of the Imaginary Unit $i$ in College Algebra

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