Complex constant from single root.

In summary, we are asked to determine the complex constant c for which the given equation has a root of v = √3 - j. After analyzing the equation and using the formula rejθ = r(cosθ + jsinθ), we can express v as an exponential and solve for c.
  • #1
DmytriE
78
0

Homework Statement


Do not use a calculator for this problem. Express your answers using square roots and/or fractional multiples of x.

Determine the complex constant c such that v is a root of: z6 - c = 0


Homework Equations


v = [itex]\sqrt{3} - j[/itex]


The Attempt at a Solution



I believe the following are true:
1. There are 3 distinct roots for this equation.
2. Each of the distinct roots will have a conjugate pair to ensure there is no middle term.
3. If 2 is true, then two of the six roots are [itex]\sqrt{3} -j[/itex] and [itex]\sqrt{3} +j[/itex]

z6 - c = 0 --> z6 = c. Yes, this is as far as I have gotten. I'm not sure how to figure out the other 4 roots.
 
Physics news on Phys.org
  • #2
c = z6
v = √3 - j
Use rejθ = r(cosθ + jsinθ)
Write v as exponential
Solve for c
 

FAQ: Complex constant from single root.

1. What is a complex constant from single root?

A complex constant from single root is a numerical value that can be represented as a combination of a real number and an imaginary number. It is derived from a single root, which is the solution to a complex equation.

2. How is a complex constant from single root calculated?

A complex constant from single root is calculated by taking the square root of the negative value inside the radical sign in the complex equation. This value is then multiplied by the complex conjugate of the denominator to eliminate the imaginary component.

3. What is the significance of a complex constant from single root in science?

In science, complex constants from single root are used to represent physical quantities that have both magnitude and direction, such as electric and magnetic fields. They are also used in signal processing, control systems, and other fields of engineering.

4. Can a complex constant from single root have a negative value?

Yes, a complex constant from single root can have a negative value. This indicates that the imaginary component is pointing in the opposite direction of the real component, and the overall value is in the fourth quadrant of the complex plane.

5. How is a complex constant from single root different from a real constant?

A complex constant from single root is different from a real constant because it includes an imaginary component, while a real constant only has a real component. This means that a complex constant from single root can have both magnitude and direction, while a real constant only has magnitude.

Similar threads

Comp Sci Recursive Double code to Calculate the sum of the square roots <= a number
Replies
19
Views
2K
Obtaining stability criterion for 2nd order ODEs in coefficient form
Replies
1
Views
742
MHB Roots of equation and probability
Replies
1
Views
929
B Principal square root of a complex number, why is it unique?
Replies
13
Views
4K
MHB Real Roots of Cubic Equation: $x^3+a^3x^2+b^3x+c^3=0$
Replies
1
Views
1K
Comp Sci Working with classes and vectors in C++
Replies
15
Views
2K
Comp Sci Complexity for generating strings of length k from CNF grammar
Replies
3
Views
1K
How Do You Implement Root-Finding for Compressibility Factors in MATLAB?
Replies
2
Views
2K
From differential equations to transfer functions
Replies
5
Views
2K
MHB Is It Possible to Prove Real Root Properties in Cubic Equations?
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top