1)Shade each region in the complex plane. Justify your solution
z - (z ̅ )=4
for this question what is (z ̅ ) stand for?
how can I solve it?
2) Find all the solution of the equation z^5+z^3+z^2+1=0
how can I factor this equation? Or there is another way to solve it?
Thanks!!
Complex number
2014-01-20 9:40 pm
回答 (2)
2014-01-20 10:31 pm
✔ 最佳答案
1) As z is a complex number, so you can assume that z = x + yi, where x, y are real and i = √-1, z ̅ means the conjugate of z, that is z ̅ = x - yi.z - (z ̅ )=4==> (x + yi) - (x - yi) = 4==> 2yi = 4As real part 0 = 4 is not true, so there is no solution for this equation.2) z^5 + z^3 + z^2 + 1 = 0==> (z^2 + 1)(z^3 + 1) = 0==> (z^2 + 1)(z + 1)(z^2 - z + 1) = 0==> z = i, -i, -1, (1 + i√3)/2, (1 - i√3)/2
2014-01-20 10:18 pm
z = a + bi where a and b are real.
z bar is called the conjugate of z
z bar = a - bi
z + z bar = 2 Re(z)
z - z bar = 2 Im(z) i
2014-01-20 14:19:51 補充：
z⁵ + z³ + z² + 1 = 0
z⁵ + z² + z³ + 1 = 0
z²(z³ + 1) + z³ + 1 = 0
(z³ + 1)(z² + 1) = 0
(z³ + 1)(z² + 1) = 0
z³ = -1 or z² = -1
Use complex number to solve.
z bar is called the conjugate of z
z bar = a - bi
z + z bar = 2 Re(z)
z - z bar = 2 Im(z) i
2014-01-20 14:19:51 補充：
z⁵ + z³ + z² + 1 = 0
z⁵ + z² + z³ + 1 = 0
z²(z³ + 1) + z³ + 1 = 0
(z³ + 1)(z² + 1) = 0
(z³ + 1)(z² + 1) = 0
z³ = -1 or z² = -1
Use complex number to solve.
收錄日期: 2021-04-13 19:55:55
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20140120000051KK00076