10) 11) Simplifying powers of i: Powers of are cyclic. Any power of can be simplified i i to 1. i,-1, -i, If you know these first 4 powers of you can figure out any power of i, i. i1 = i -1 i2 = = i3 i2i1=-i 1 i4 = i2i2= Watch what happens as we continue: 1i i5 = i4i = = i = -1 i6 =i4i2 =1(-1) = i7 i4i3=-i 1 i8 = i4i4= The powers of cycle every fourth power. We can use this to find any power of i i. = -1 i14= i12i2 = (i4)3i2=1(-1) 1i i33 = i32i = = i i12 i31 i-2 i50
10) 11) Simplifying powers of i: Powers of i are cyclic. Any power of i can be simplified to i,-1, -i, 1. If you know these first 4 powers of i, you can figure out any power of i. i1 = i i2 = -1 i3 = i2i1=-i i4 = i2i2= 1 Watch what happens as we continue: i5 = i4i = 1i = i i6 =i4i2 =1(-1) = -1 i7 = i4i3=-i i8 = i4i4= 1 The powers of i cycle every fourth power. We can use this to find any power of i. i14= i12i2 = (i4)3i2=1(-1) = -1 i33 = i32i = 1i = i i12 i31 i-2 i50