How do you simplify #i^36#? Precalculus Complex Numbers in Trigonometric Form Powers of Complex Numbers 1 Answer Alan P. Nov 20, 2015 #i^36=1# Explanation: #i^2=-1# #i^4 = (i^2)^2 = (-1)^2 = 1# #i^36 = (i^4)^9 = 1^9 = 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 11570 views around the world You can reuse this answer Creative Commons License