Example i⁹
Find the remainder of 9 ÷ 4. That is the location on the power of i circle.
9 ÷ 4 = 2 R1, so i⁹ = i
i¹⁹
19 ÷ 4 = 4 R3; Remainder 3 means i³ = −i.
Easy
Powers of i. Divide the exponent by 4.
Find the remainder of 6 ÷ 4. That is the location on the power of i circle.
6 ÷ 4 = 1 R2; Remainder 2 means i² = −1.
i⁶ = −1
Answer: −1
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Find the remainder of 13 ÷ 4. That is the location on the power of i circle.
13 ÷ 4 = 3 R1; Remainder 1 means i¹ = i.
i¹³ = i
Answer: i
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Find the remainder of 8 ÷ 4. That is the location on the power of i circle.
8 ÷ 4 = 2 R0; Remainder 0 means i⁴ = 1.
i⁸ = 1
Answer: 1
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Find the remainder of 23 ÷ 4. That is the location on the power of i circle.
23 ÷ 4 = 5 R3; Remainder 3 means i³ = −i.
i²³ = −i
Answer: −i
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Find the remainder of 18 ÷ 4. That is the location on the power of i circle.
18 ÷ 4 = 4 R2; Remainder 2 means i² = −1.
i¹⁸ = −1
Answer: −1
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Find the remainder of 25 ÷ 4. That is the location on the power of i circle.
25 ÷ 4 = 6 R1; Remainder 1 means i¹ = i.
i²⁵ = i
Answer: i
Medium
Larger exponents. Same remainder after dividing by 4.
Find the remainder of 101 ÷ 4. That is the location on the power of i circle.
101 ÷ 4 = 25 R1; Remainder 1 means i¹ = i.
i¹⁰¹ = i
Answer: i
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Find the remainder of 124 ÷ 4. That is the location on the power of i circle.
124 ÷ 4 = 31 R0; Remainder 0 means i⁴ = 1.
i¹²⁴ = 1
Answer: 1
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Find the remainder of 147 ÷ 4. That is the location on the power of i circle.
147 ÷ 4 = 36 R3; Remainder 3 means i³ = −i.
i¹⁴⁷ = −i
Answer: −i
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Find the remainder of 210 ÷ 4. That is the location on the power of i circle.
210 ÷ 4 = 52 R2; Remainder 2 means i² = −1.
i²¹⁰ = −1
Answer: −1
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Find the remainder of 265 ÷ 4. That is the location on the power of i circle.
265 ÷ 4 = 66 R1; Remainder 1 means i¹ = i.
i²⁶⁵ = i
Answer: i
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Find the remainder of 288 ÷ 4. That is the location on the power of i circle.
288 ÷ 4 = 72 R0; Remainder 0 means i⁴ = 1.
i²⁸⁸ = 1
Answer: 1
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