# If z3−1=0z3-1=0, then we are looking for the cubic roots of unity, i.e. the numbers such that z3=1z3=1.

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Using DeMoivre’s Theorem Assignment | Assignment Help Services
Just from $13/Page If you’re using complex numbers, then every polynomial equation of degree kk yields exactly kk solution. So, we’re expecting to find three cubic roots. De Moivre’s theorem uses the fact that we can write any complex number as ρeiθ=ρ(cos(θ)+isin(θ))ρeiθ=ρ(cos(θ)+isin(θ)), and it states that, if z=ρ(cos(θ)+isin(θ))z=ρ(cos(θ)+isin(θ)), then zn=ρn(cos(nθ)+isin(nθ))zn=ρn(cos(nθ)+isin(nθ)) If you look at 11 as a complex number, then you have ρ=1ρ=1, and θ=2πθ=2π. We are thus looking for three numbers such that ρ3=1ρ3=1, and 3θ=2π3θ=2π. Since ρρ is a real number, the only solution to ρ3=1ρ3=1 is ρ=1ρ=1. On the other hand, using the periodicity of the angles, we have that the three solutions for θθ are θ1,2,3=2kπ3θ1,2,3=2kπ3, for k=0,1,2k=0,1,2. This means that the three solutions are: 1. ρ=1,θ=0ρ=1,θ=0, which is the real number 11. 2. ρ=1,θ=2π3ρ=1,θ=2π3, which is the complex number 12+3–√2i-12+32i 3. ρ=1,θ=4π3ρ=1,θ=4π3, which is the complex number 123–√2i Calculate your paper price Pages (550 words) Approximate price: - Why Choose Us Quality Papers At Myhomeworkwriters.com, we always aim at 100% customer satisfaction. As such, we never compromise o the quality of our homework services. Our homework helpers ensure that they craft each paper carefully to match the requirements of the instruction form. Professional Academic Writers With Myhomeworkwriters.com, every student is guaranteed high-quality, professionally written papers. We ensure that we hire individuals with high academic qualifications who can maintain our quality policy. These writers undergo further training to sharpen their writing skills, making them more competent in writing academic papers. Affordable Prices Our company maintains a fair pricing system for all academic writing services to ensure affordability. Our pricing system generates quotations based on the properties of individual papers. On-Time delivery My Homework Writers guarantees all students of swift delivery of papers. We understand that time is an essential factor in the academic world. Therefore, we ensure that we deliver the paper on or before the agreed date to give students ample time for reviewing. 100% Originality Myhomeworkwriters.com maintains a zero-plagiarism policy in all papers. As such, My Homework Writers professional academic writers ensure that they use the students’ instructions to deliver plagiarism-free papers. We are very keen on avoiding any chance of similarities with previous papers. Customer Support 24/7 Our customer support works around the clock to provide students with assistance or guidance at any time of the day. Students can always communicate with us through our live chat system or our email and receive instant responses. Feel free to contact us via the Chat window or support email: support@myhomeworkwriters.com. Try it now! ## Calculate the price of your order You will get a personal manager and a discount. We'll send you the first draft for approval by at Total price:$0.00

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