Question 1

Which of the following is the value of $$i^{23}$$?

Accepted Answer

$$i$$

Question 2

A medical imaging device uses the value $$i^{100} in $$its calculations. What is the simplified value?

Accepted Answer

$$1$$

Question 3

Which of the following is equivalent to $$i^{57}$$?

Accepted Answer

$$-i$$

Question 4

A chemical reaction simulation uses $$i^{2023}. $$What is the simplified value?

Accepted Answer

$$-i$$

Question 5

Which of the following is the correct simplification for $$i^{0}$$?

Accepted Answer

$$1$$

Question 6

If $$i^{n} = -1$, which of the following could be the value of n$?

Accepted Answer

$$14$$

Question 7

A student claims that $$i^{15} = 1$. Is this correct?

Accepted Answer

No, $$i^{15} = i$

Question 8

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

Accepted Answer

$$i$$

Question 9

A circuit design uses $$i^{44}. $$What is the simplified value?

Accepted Answer

$$1$$

Question 10

Which of the following is the value of $$i^{73}$$?

Accepted Answer

$$-1$$

Question 11

A student is asked to simplify $$i^{4n+2}$$ for any integer $$n. $$What is the result?

Accepted Answer

$$-1$$

Question 12

Which of the following is the value of $$i^{999}$$?

Accepted Answer

$$-i$$

Question 13

A student simplifies $$i^{4k}$$ for any integer $$k. $$What is the result?

Accepted Answer

$$1$$

Question 14

Which of the following is the value of $$i^{28}$$?

Accepted Answer

$$1$$

Question 15

A student claims that $$i^{4m+3} = -i$ for any integer m$. Is this correct?

Accepted Answer

Yes, $$i^{4m+3} = -i$

Question 16

Which of the following is the value of $$i^{45}$$?

Accepted Answer

$$i$$

Question 17

A student is asked to simplify $$i^{4n+1}$$ for any integer $$n. $$What is the result?

Accepted Answer

$$i$$

Question 18

Which of the following is the value of $$i^{102}$$?

Accepted Answer

$$-1$$

Question 19

A student is asked to simplify $$i^{4n+0}$$ for any integer $$n. $$What is the result?

Accepted Answer

$$1$$

Question 20

Which of the following is the value of $$i^{101}$$?

Accepted Answer

$$i$$

Powers of i: Simplifying Complex Number Exponents

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