Square roots of complex number Watch

Super199
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Question: Find the square roots of 8root3i-8

z= 16cos(pi/3+isinpi/3)
z^1/2 = 4cos(pi/6+ isinpi/6)
z^1/2 = +- 4( root3/2 + 1/2i)
z^1/2 = +-2root+2i?
Is that right.

Btw is this using de moivre's theorem because it isn't mentioned till a later chapter in the book.

cheers
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Monsor
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(Original post by Super199)
Question: Find the square roots of 8root3i-8

z= 16cos(pi/3+isinpi/3)
z^1/2 = 4cos(pi/6+ isinpi/6)
z^1/2 = +- 4( root3/2 + 1/2i)
z^1/2 = +-2root+2i?
Is that right.

Btw is this using de moivre's theorem because it isn't mentioned till a later chapter in the book.

cheers

Bro you're meant to use Charles Darwin's theory about evolution

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B_9710
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It is De Movire's theorem. Sometimes you may find it quicker and more convenient to express complex numbers in exponential form,  e^{i\theta} . But yeah everything you've done is fine.
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Super199
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(Original post by Monsor)
Bro you're meant to use Charles Darwin's theory about evolution

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snm
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Zacken
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I don't think that's quite right (at a glance can't check for sure) and it is using DeMoivre's. You might want to haveanother go using (a+ib)^2 = -8 + 8rt(3)i and gettig two simultaneous equations by comparing real and imaginary.
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Super199
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(Original post by Zacken)
I don't think that's quite right (at a glance can't check for sure) and it is using DeMoivre's. You might want to haveanother go using (a+ib)^2 = -8 + 8rt(3)i and gettig two simultaneous equations by comparing real and imaginary.
Yh I would have lol but I don't think you can in FP3
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Zacken
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(Original post by Super199)
Yh I would have lol but I don't think you can in FP3
You certainly can.
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Super199
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(Original post by Zacken)
You certainly can.
But obvs for higher powers its better to use de moivre's theorem?
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B_9710
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Sorry, I didn't actually check your answer for some reason but as Zacken thinks there is a mistake, you can bet there must be.
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Zacken
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(Original post by Super199)
But obvs for higher powers its better to use de moivre's theorem?
Any power higher than 2 is almost impossible using the simultaneous method and DeMoivre is a necessity, yes. Anywho, I'm not sure your answer is corrct. So check it using the other method I suggested.
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Zacken
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(Original post by B_9710)
Sorry, I didn't actually check your answer for some reason but as Zacken thinks there is a mistake, you can bet there must be.
Don't take my word for it! I'm in bed and half asleep. :laugh:
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