How do you simplify i^102? Precalculus Complex Numbers in Trigonometric Form Powers of Complex Numbers 1 Answer Tom Nov 12, 2015 i^102 = -1 Explanation: 102 = 2*51 i^102 = (i^2)^51 = (-1)^51 = -1 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 9036 views around the world You can reuse this answer Creative Commons License