# How do you find the radial value?

1. Apr 19, 2007

### princiebebe57

What is the radial value for the 3rd root of the complex number 4 + -2i ?

2. Apr 19, 2007

### J77

Did they teach you Euler's formula and De Moivre?

3. Apr 19, 2007

### princiebebe57

De Moivre's Theorem

4. Apr 19, 2007

### J77

So, you know how to write the complex number in exponential form?

5. Apr 19, 2007

### princiebebe57

Can you refresh my memory please?

6. Apr 19, 2007

### J77

Euler says that a complex number can be written as $$z=re^{i\phi}$$, where r is the absolute value of z.

What is r in your case?

7. Apr 19, 2007

### princiebebe57

r = 2 square root of 5?

8. Apr 19, 2007

### J77

Yep -- $$\sqrt{20}$$. So what's the 3rd root of r?

9. Apr 19, 2007

### princiebebe57

that's where im stuck. how do you do that?

10. Apr 19, 2007

### J77

De Moivre: $$z^n=(re^{i\phi})^n=r^ne^{in\phi}$$

11. Apr 19, 2007

### princiebebe57

i'm lost...=/

12. Apr 19, 2007

### J77

For the 3rd root, what's n in my previous post?

13. Apr 19, 2007

### princiebebe57

it's 3 right?

14. Apr 19, 2007

### J77

Nope -- what's a sqaure root expressed as a power?