- #1
cotufa
- 16
- 0
Homework Statement
Solve
[tex]
z^3 - 3z^2 + 6z - 4 = 0
[/tex]
The Attempt at a Solution
I tried factoring a z and quadratic equation but went nowhere
Input apreciated
cotufa said:Homework Statement
Solve
[tex]
z^3 - 3z^2 + 6z - 4 = 0
[/tex]
The Attempt at a Solution
I tried factoring a z and quadratic equation but went nowhere
Input apreciated
gabbagabbahey said:Well there is a constant term in the equation, so z is clearly not a factor.
The first thing to take note of is that this is a 3rd degree polynomial and so there must be 3 roots. Moreover, at least one of those roots must be real. So try to find a real root by inspection: plug in z=0, z=1, z=-1, z=2...etc. until you find a root z_0 and then factor out a (z-z_0) to obtain a quadratic equation you can then solve to find the other two roots.
A complex number equation is an equation that includes both real and imaginary numbers. It is written in the form of a + bi, where a is the real number and bi is the imaginary number.
To solve a complex number equation, you can use the properties of complex numbers, such as the distributive property, to simplify the equation. Then, you can use the quadratic formula or other methods to find the values of the variables.
A real number equation only includes real numbers, while a complex number equation includes both real and imaginary numbers. Real numbers can be represented on a number line, while complex numbers have a real part and an imaginary part.
Yes, a complex number equation can have multiple solutions. This is because the equation can have multiple values for the variables that satisfy the equation. These solutions can be represented as points on a complex plane.
Complex number equations are used in many fields of science, such as physics and engineering, to model and solve real-world problems. They are particularly useful in analyzing systems with oscillatory behavior, such as electrical circuits and wave phenomena.