mathscomplex numbers
posted by Anonymous .
by using the substitution w = z^3, find all the solutions to z^6  8z^3 +25 = 0 in complex numbers, and describe them in polar form, using @(theta) to denote the angle satisfying tan@ = 3/4 ( note simply leave @ as it is, don't calculate it).
i got up to z^3 = 4+3i and 43i then got stuck !
4 + 3i = 5 Exp[i theta]
The equation z^3 = Q for real positive Q has three solutions:
z = cuberoot[Q] Exp[2 pi n i/3]
for n = 0, 1 and 2, because
Exp[2 pi n i/3]^3 = Exp[2 pi n i] = 1
So, in this case you find:
z = 5^(1/3) Exp[i theta/3 + 2 pi n i/3 ]
Respond to this Question
Similar Questions

complex numbers
3 + 4i in polar form in pi the magnitude is 5 from pyth theorm. Now the angle. Using i the positive real as the reference axis, the angle from it is PI/2 + arctan4/3 
Maths complex numbers
Find tan(3 theta) in terms of tan theta Use the formula tan (a + b) = (tan a + tan b)/[1  tan a tan b) in two steps. First, let a = b = theta and get a formula for tan (2 theta). tan (2 theta) = 2 tan theta/[(1  tan theta)^2] Then … 
Abstract Algebra
Let H={a+bi a,b is a element R, a^2+b^2=1} be a subset of the non zero complex numbers C*. Prove that H<C* under complex multiplication using the onestep subgroup test. Also describe the elements of H geometrically. 
maths (complex numbers)
if b is a real number satisfying b^4 + 1/(b^4) = 6, find the value of : (b + i/b)^16 where i = sqrt of 1 
Math (Complex Numbers)
Let a,b,c be complex numbers satisfying a+b+c=abc=1 and (ab+bc+ac)/3=(1/a^2)+(1/b^2)+(1c^2) The sum of absolute values of all possible ab+bc+ac can be written as (√n)/m, where n and m are positive coprime integers. What is n+m? 
Complex Numbers
The system of equations z  2  2i = \sqrt{23}, z  8  5i = \sqrt{38} has two solutions z1 and z2 in complex numbers. Find (z1 + z2)/2. Im really just plain old confused. Could anyone help me out? 
Precal
The equation of the line joining the complex numbers 5 + 4i and 7 + 2i can be expressed in the form az + b*overline{z} = 38 for some complex numbers a and b. Find the product ab. Any help? 
Maths
Have a question on complex numbers. Z1= 1+j2, Z2= 2+j5 Find total impedance in Cartesian and polar form of two impedances in parallel: 1/ZT = 1/Z1 + 1/Z2 I get to 39/58 + 83/58 j but then get a bit lost. 
Roots, complex numbers
I want to solve z^5=1 But all the examples I've seen use positive numbers. The 1 is throwing me off somewhat. Most of the examples I've worked with would be solved using the polar form I.e Z^5(cos5+i sin5)=1(cospi +i sinpi) But as … 
Linear algebra
Find all complex numbers z satisfying z3 = 27i and give your answer as a commaseparated list of values in the form a+bi.