If w is a complex root of z7 - 1 = 0. .5 z 3 Show that w is a solution of 2 z z z z 1 = 0. i. Find a quadratic equation with real coefficients having a root www ii. 2т Зп 1 TT iii. Prove that cos 7 COS 7 COS 7 2

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A: Given are the roots of a characteristic equation    1±3i,1±3i⏟,  2,2,2,2,4⏟       Repeated…

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Q: 5. Find the general solutions of the equations i) Zx - 4z,, – 5z, +10z, = cos(x+3y)-sin(x+3y) %3D

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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A: Given,                           z''+z'+z=teit                                 (1)

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Q: Which of the following is a fundamental set of solution of y" – 2y' + 5y = 0. {e' cos 2t, e' sin 2t}…

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A: Given  a= 2 ,b=6 ,c= 17  x= 1 and y=6 x+iy= 1+6i

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Q: 5. Find the general solutions of the equations i) Z - 4z, - 5z, +10z, = cos(x+3y)-sin(x+3y) %3D ii)…

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Q: 4.3 Use the calculus of residues to evaluate the following integral 2 1 1+8 cos? 0

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