How do you find the radial value?

[princiebebe57]

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

 

[J77]

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

 

[princiebebe57]

De Moivre's Theorem

 

[J77]

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

 

[princiebebe57]

Can you refresh my memory please?

 

[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?

 

[princiebebe57]

r = 2 square root of 5?

 

[J77]

r = 2 square root of 5?

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

 

[princiebebe57]

that's where I am stuck. how do you do that?

 

[J77]

that's where I am stuck. how do you do that?

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

 

[princiebebe57]

i'm lost...=/

 

[J77]

i'm lost...=/

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

 

[princiebebe57]

it's 3 right?

 

[J77]

it's 3 right?

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