How do you find fifth roots of #1#? Trigonometry The Polar System The Trigonometric Form of Complex Numbers 1 Answer Rhys Jun 26, 2018 #=> z = e^(2/5 k pi i ) # # k ={0,1,2,3,4} # Explanation: We are hence find #z# if #z = root5 1 # #=> z^5 = 1# Use how #e^(2kpi i ) =1 , AA k in ZZ # Hence #z^5 = e^(2kpi i ) # #=> z = e^(2/5 k pi i ) # For # k ={0,1,2,3,4} #, As any other #k# will give related solutions Where # re^(i theta ) = rcostheta+ irsintheta# Answer link Related questions What is The Trigonometric Form of Complex Numbers? How do you find the trigonometric form of the complex number 3i? How do you find the trigonometric form of a complex number? What is the relationship between the rectangular form of complex numbers and their corresponding... How do you convert complex numbers from standard form to polar form and vice versa? How do you graph #-3.12 - 4.64i#? Is it possible to perform basic operations on complex numbers in polar form? What is the polar form of #-2 + 9i#? How do you show that #e^(-ix)=cosx-isinx#? What is #2(cos330+isin330)#? See all questions in The Trigonometric Form of Complex Numbers Impact of this question 11488 views around the world You can reuse this answer Creative Commons License