Cube roots

Kiran · 2006-12-11 11:36:34

find the three cube roots of -7 + 5i and express the roots in polar coordinates

ok i got stuck

R = sqrt(-7^2 + 5^2)
R = 4.898979486
R = 4.90

tan(theta) = -7/5
theta = ..............what???next
i dont know how ot do the next part...what does theta equal to?

gnitsuk · 2006-12-11 23:59:32

The numbers here aren't very nice. You need to be comfortable with expressing complex numbers in exponential form:

So

can be written as:

Where r is the modulus of the complex number and

is the argument of the complex number.

So in your case:

and

So we can write:

Now we take the cube root of each side to give:

Now that we have the values of i and

for our cube root it is easy enough to substitute them into the polar formula:

Last edited by gnitsuk (2006-12-13 00:55:13)

Kiran · 2006-12-12 09:10:23

this is very complex work

LQ · 2006-12-13 00:34:13

Must help gnitsuk... Wrote:

Should be:

This is not good. Personally, I think the equations are a wee bit harder then the numbers

I would also like to add that i remember a certain rule (r(cos(Q) + isin(Q)))^p = r^p(cos(pQ)+isin(pQ))

I would like to have that verified.

Last edited by LQ (2006-12-13 00:35:59)

gnitsuk · 2006-12-13 00:55:01

Quite right. Simple Typo. Have corrected it. Thanks.

LQ · 2006-12-13 01:04:43

Thank you for showing us this though, I'd almost forgotten all about it!

Last edited by LQ (2006-12-13 01:05:14)

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