Wednesday
January 28, 2015

# Homework Help: maths-complex numbers

Posted by Anonymous on Monday, March 12, 2007 at 9:25am.

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, dont calculate it).

i got up to z^3 = 4+3i and 4-3i 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 ]

Related Questions

Pre-cal - The equation of the line joining the complex numbers -5 + 4i and 7 + ...
Complex Numbers - The system of equations |z - 2 - 2i| = \sqrt{23}, |z - 8 - 5i...
Abstract Algebra - Let H={a+bi a,b is a element R, a^2+b^2=1} be a subset of the...
Mathematics - Express the Complex Number -1-i in polar form. how is complex no ...
complex numbers - -3 + 4i in polar form in pi the magnitude is 5 from pyth ...
math-complex numbers - Sketch the sets of complex numbers in the complex plane ...
Algebra - Find all complex numbers z such that z^2=2i. Write your solutions in ...
Math (Complex Numbers) - Let a,b,c be complex numbers satisfying a+b+c=abc=1 and...
Precalculus - Let z and w be complex numbers such that |2z - w| = 25, |z + 2w...
calculus - can you please explain tep by step how to solve dividing complex ...

Members