De Moivre's Theorem

greatwhiteshark

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Joined
May 8, 2005
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279
Write each expression in the standard form: a +bi.

(sqrt2 - i)^6

I found the radius to be sqrt3.

I used the sine function to find the reference angle, which is:
-sqrt3/3. However, I DO NOT recognize this fraction for sine. If I cannot find the reference angle, I cannot find theta, which I need to use in
De Moivre's Theorem.
 
x=a+bi
R= [a^2+b^2]^1/2
@=tan ^-1 (b/a)

let a=sqrt2
b=-1
R=[2+1]^1/2
R= sqrt3
@= tan^-1 [ -1/sqrt2]
@=-35.26degrees

then x^6 = R^6,6*@ answer
please check math
Arthur
 
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