How do you find the radial value?

In summary, the conversation discusses the concept of writing a complex number in exponential form using Euler's formula and De Moivre's Theorem. The radial value for the 3rd root of a complex number is determined by taking the absolute value of the complex number and raising it to the power of n. The conversation also touches on the concept of expressing square roots as powers.
  • #1
princiebebe57
31
0
What is the radial value for the 3rd root of the complex number 4 + -2i ?
 
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  • #2
Did they teach you Euler's formula and De Moivre?
 
  • #3
De Moivre's Theorem
 
  • #4
So, you know how to write the complex number in exponential form?
 
  • #5
Can you refresh my memory please?
 
  • #6
Euler says that a complex number can be written as [tex]z=re^{i\phi}[/tex], where r is the absolute value of z.

What is r in your case?
 
  • #7
r = 2 square root of 5?
 
  • #8
princiebebe57 said:
r = 2 square root of 5?
Yep -- [tex]\sqrt{20}[/tex]. So what's the 3rd root of r?
 
  • #9
that's where I am stuck. how do you do that?
 
  • #10
princiebebe57 said:
that's where I am stuck. how do you do that?
De Moivre: [tex]z^n=(re^{i\phi})^n=r^ne^{in\phi}[/tex]
 
  • #11
i'm lost...=/
 
  • #12
princiebebe57 said:
i'm lost...=/
For the 3rd root, what's n in my previous post?
 
  • #13
it's 3 right?
 
  • #14
princiebebe57 said:
it's 3 right?
Nope -- what's a sqaure root expressed as a power?
 

FAQ: How do you find the radial value?

How do you define the radial value in scientific terms?

The radial value is defined as the distance from the center of an object to a specific point on its surface. It is commonly used in physics and engineering to describe the size and position of objects.

What is the mathematical formula for calculating the radial value?

The mathematical formula for calculating the radial value is r = √(x^2 + y^2 + z^2), where r is the radial value, and x, y, and z are the coordinates of the point on the object's surface.

How do you measure the radial value in real-life scenarios?

The radial value can be measured using various tools such as rulers, calipers, and measuring tapes. In more complex scenarios, specialized equipment such as laser scanners or coordinate measuring machines may be used.

What is the significance of radial value in scientific research?

The radial value is an important aspect of scientific research as it helps scientists understand the size, shape, and position of objects. It is also crucial in making accurate measurements and calculations in various fields, including astronomy, physics, and engineering.

Can the radial value change over time?

Yes, the radial value can change over time. This is especially true for objects that are constantly moving or undergoing changes in size or shape. It is essential to consider these changes when conducting scientific experiments or making calculations based on the radial value.

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