How do you simplify i^1005? Precalculus Complex Numbers in Trigonometric Form Powers of Complex Numbers 1 Answer Shura Apr 1, 2016 i^1005 = i^1004 * i = (i^2)^502 * i = (-1)^502 * i = 1 * i = i. Answer link Related questions How do I use DeMoivre's theorem to find (1+i)^5? How do I use DeMoivre's theorem to find (1-i)^10? How do I use DeMoivre's theorem to find (2+2i)^6? What is i^2? What is i^3? What is i^4? How do I find the value of a given power of i? How do I find the nth power of a complex number? How do I find the negative power of a complex number? Write the complex number i^17 in standard form? See all questions in Powers of Complex Numbers Impact of this question 2959 views around the world You can reuse this answer Creative Commons License