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# how to solve chapter 7 of higher trigonometry by b.c. das

find the general value of Ø which satisfies the equation                                         (cosØ+isinØ)( cos2Ø+isin2Ø)...(cosnØ+isin nØ)=1

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## Suggested Questions And Answer :

### how to solve chapter 7 of higher trigonometry by b.c. das

Applying de Moivre's Theorem, (cos nx + i sin nx) = (cos x + sin x)^n, almost the only way to make this equation valid is for all the factors equal to 1. That means cos ø + i sinø = 1 so   ø = 2pi z, where z is an integer. But when ø = pi/2 + 2pi z, the cosines drop out and we get the expression i * i^2 * i^3 * i^4 etc. That gives us a repeating pattern of i, -1, -i, 1 depending on the value of n. So this value for  ø can only be used when n = 4N where N is an integer.

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komplex numbers...if yu wanna raes it tu a power & root fist, konvert tu exponenshal form (1+i)...leng=root(2) & ange=45 deg, & that bekum...pi/4 so yer number=root(2)*e^(pi/4)i power=(1/4) or 4th root...size=root(2)^1/4=2^1/8 angel=(1/4)*(pi/4)=pi/16 radians size...2^0.125=1.0905077326652577 angel...pi/16=0.19634954084936207 radians anser...1.0905077326652577*e^0.19634954084936207i

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yu dont, tu "solv" yu need equashun such as x^3+125=0 Then x^3=-125 & x=kube root(-125) y= -5

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1 1 1 | 140  3 4 8 | 840  1 -2 0| 0  Now if you can use the calculator to solve, you would get the identity matrix on the left.  By hand, it is a longer process.  When you get  | 1 0 0 | 40|  | 0 1 0 | 20|  | 0 0 1 | 80|  X= 40; y= 20; z= 80  Checking: 40+20+80= 140  3(40)+ 4(20) + 8(80)= 840 dollars  And 40= 2(20)

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5(5+i)/(2+i)(1-i)

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I am confused. You mean to say, how would this be possible? If so, then y would have to be -18 or higher. This is so because if y is -18 and you add it to 6, it is -12. -12 is greater than -13, therefore hopefully answering your question.

### Please show me how to solve 1/3=9^2x-5

me assume thats spozed tu be 9^2x -5=1/3 or 9^2x=5& 1/3 =5.33333333333... log(9^2x)=2x*log(9) =log(5.3333333) so 2x=log(5.333333) / log(9) =0.726998727 / 0.954242509 =0.761859506