Aim: How can we simplify powers of i? The powers of i repeat in a definite cycle: i, -1, -i, 1 By definition i0 = 1. Therefore: i0 = 1 i1 = i i2 = -1 i3 = -i i4 = 1 i5 = i i6 = -1 i7 = -i i8 = 1 i9 = i i10 = -1 i11 = -i i12 = 1 i13 = i i14 = -1 i15 = -i Using and i2 = -1.

Aim: How can we simplify powers of i? If a whole number exponent is divided by 4, the remainder is 0, 1, 2, or 3. We can simplify powers of i by using the remainders after dividing by 4. Example: Write i82 in simplest terms 82 = 20 remainder 2 4 Therefore i82 is equivalent to i2. So i82 = -1

Aim: How can we simplify powers of i? Write each given power of I in simplest terms, as 1, i, -1, or -i i12 i91 i49 i54

Aim: How can we simplify powers of i? Write each given power of I in simplest terms, as 1, i, -1, or -i i12 = i0 = 1 2. i91 = i3 = -i 3. i49 = i1 = i 4. i 54 = i2 = -1

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