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ONE OR MORE CORRECT If complex no. (1+ri)^3=S(1+i)for some real S then value of r can be A cos pi/5 B cosec 3pi/2 C cot pi/12 D tan pi/12

nitish krishnatra , 14 Years ago
Grade 12th Pass
anser 1 Answers
Chetan Mandayam Nayakar

let (1+ri)^3=x+iy

argument of x+iy=3*arctan(3)

argument of S(1+i)=(pi/4)+(n*pi), where n is ANY integer

3arctan(r)=pi/4 +n*pi

arctan(r)=(pi/12)+(n/3)*pi

r=tan((pi/12)+(n*pi/3)), for ANY INTEGER n

 

 

 

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