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If [sqrt(3) +1] 100 = 2 99 (a+ib) then b= ? ….….….….…....

If [sqrt(3) +1]100 = 299(a+ib) then b= ?
….….….….…....

Grade:11

1 Answers

Aamina
64 Points
7 years ago
[sqrt(3)+i]100=299(a+ib)
 
[2(sqrt(3)/2+i/2)]100=299(a+ib)
 
2100[sqrt(3)/2+i/2]100=299(a+ib)
 
2[ cos\tiny \prod/6 + i sin\tiny \prod/6 ]100=(a+ib)
 
2[cos 100\tiny \prod/6 + i sin100\tiny \prod/6]=(a+ib)         [from de moivre’s theorem]
 
2[cos 50\tiny \prod/3 +i sin50\tiny \prod/3]=(a+ib)
 
2[cos(16\tiny \prod + 2\tiny \prod/3) + i sin (16\tiny \prod +2\tiny \prod/3) ] =(a+ib)
 
2[cos 120 + i sin 120] =(a+ib)
 
2[-1/2 +i sqrt(3)/2 ]=(a+ib)
 
-1 + i sqrt(3) = (a+ib)
 
on comparing real and imaginary parts ,we get a= -1 and b=sqrt(3)
 

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