Trignometry
posted by hello .
Solve the equation. Express your answer in trigonometric form.
x^511=0
I know the answer is:
11^1/5(cos α + i sin α) for α = 0°, 72°, 144°, 216°, 288°.
But I don't know where to even start working on this problem.

Huh? You have all the answers!
If you let r = 11^(1/5), the numbers are
r cis 0°
r cis 72°
...
The n * (cosθ + i sinθ) is the trigonometric or polar form.
a + bi is the complex or rectangular form.
Hmmm. I see that you don't know how to arrive at the answers. Well, if z = r cisθ, then
z^n = r^n * cis(nθ)
Since x^511=0 has 5 solutions, they must all be solutions to
z = 11^(1/5)
It appears that there is only one solution, but that is because there is only one real solution. There must also be 4 complex solutions, and if plotted, they all lie on the circle with radius 11^(1/5).
We want all the distinct points which lie on this circle, such that
z^5 = 11
11 = 11 cis 0°
But, 11 is also
11 cis 360°
11 cis 720°
...
We want solutions where z^5 puts us back on the real axis. If we go around 1,2,3,4 times, we wind up back where we started.
So, if z = 11^(1/5) cis72°,
z^5 = 11 cis 360°, so that is our 2nd root.
Taking increments of 72°, we get all the points on the circle which wind up back on the real axis if the angle is multiplied by 5.
Don't know whether that helps. If you can't follow the discussion in your textbook, I'm not sure I can make it any clearer. Do a web search on complex roots and see what hits you get. 
Ok i ll do research on it. Thank you very much for your help.
Respond to this Question
Similar Questions

Calculus  Challenge question
Our teacher gave us this problem as a challenge. Some of us have been working on it for a few days help! Prove that the largest area of any quadrilateral is obtained when opposite angles are supplementary. Wow, what a classic and nice … 
Math
If α and β are two angles in Quadrant II such that tan α= 1/2 and tan β = 2/3, find cos(α+β) Work: cos(α+β) = [ 1  (tan α)(tan β) ] / [ 1 + (tan α)(tan β)] cos(α+β) … 
Physics
The index of refraction of the core of a typical fiber optic is ncore = 1.46; the cladding has nclad = 1.4. Calculate the critical angles for the total internal reflection i crit and α crit. I have verified the answer for i crit … 
trig
Please help me! SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Verify that each equation is an identity. (sec α + tan α)^2 = 1 + sin α/1  sin α 
physics
In Physics, it is important to use mathemat ical approximations. For instance, in a small angle approximation, tan α ∼ sin α . Find the largest angle α for which the dif ference of sin α − tan α … 
Trig
prove sin(α+β)sin(αβ)=cos^2βcos^2α please help... this is the only one I didn't understand out of all my homework... 
Math Trigonometry
Given w=2+2i and v=−5√3+5i, vw^2 can be expressed as r*(cos(α∘)+i*sin(α∘)), where r is a real number and 0≤α≤360. What is the value of r+α? 
Math (Trigonometry [Polar Form])
Let z be a complex number such that z = 2(cos 8∘ + i cos 82∘).Then z^5 can be expressed as r(sin α∘+ i cos α∘), where r is a real number and 0 ≤ α ≤ 90. What is the value of r+α? 
Pure Mathematics
4) The roots of the equation z^2+2z+4=0 are denoted by α and β. a) find α and β in the form re^iθ, giving the values of r and θ b) Using de Moivre's Theorem, show that α^3=β^3. c) find the exact … 
Trigonometry
find the exact value of sin 2α if cos α=4/5 (α in quadrant I)