Complex Numbers

Powers of i

i, i², i³, i⁴ = 1, cyclically

  • High school
  • about 2 min
  • 12 of 18 in the family
Not started
i^0=1i^1=ii^2=-1i^3=-i

Power n

1
i1=i1=ii^{1} = i^{1} = i
i4k=1,  i4k+1=i,  i4k+2=−1,  i4k+3=−ii^{4k} = 1,\; i^{4k+1} = i,\; i^{4k+2} = -1,\; i^{4k+3} = -i

i is a 90° rotation. Four rotations = 360° = back to start. That's why the cycle i, i², i³, i⁴=1 repeats forever.