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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?
Live 4 Love
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The numbers here aren't very nice. You need to be comfortable with expressing complex numbers in exponential form:
http://www.mathcentre.ac.uk/students.ph … resources/
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)
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this is very complex work
Live 4 Love
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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)
I see clearly now, the universe have the black dots, Thus I am on my way of inventing this remedy...
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Quite right. Simple Typo. Have corrected it. Thanks.
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Thank you for showing us this though, I'd almost forgotten all about it!
Last edited by LQ (2006-12-13 01:05:14)
I see clearly now, the universe have the black dots, Thus I am on my way of inventing this remedy...
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