How do you use the exponent to determine the simplified form of any power of i? Precalculus Complex Numbers in Trigonometric Form Powers of Complex Numbers 1 Answer A. S. Adikesavan Nov 29, 2016 #i^(2n)=(-1)^n=+-1#, according as n is even or odd. #i(2n+1)=(-1)^ni=+-i#, according as n is even or odd. Explanation: Use #i^2=-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 #n#th 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 1265 views around the world You can reuse this answer Creative Commons License