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If alpha "and" beta "are roots "x^2-2x+4...

If `alpha "and" beta "are roots "x^2-2x+4=0 "then show that"alpha^n+beta^n=2^(n+1)"cos"(npi)/3`

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MBD PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-QUESTION BANK
  1. Solve the equationz^3=1+i

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  2. Given cos alpha+cos beta +cos gamma=sin alpha+sin beta +sin gamma=0 S...

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  3. If sin alpha + sin beta +sin gamma=0 =cos alpha+cos beta+cos gamma=0 "...

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  4. If x+1/x=2cos theta,"Show that"x^n+1/x^n=2cos n theta

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  5. xr=cos alphar+isinalphar. r=1,2,3 "and" x1+x2+x3=0 "Show that" 1/x1+1...

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  6. Show that ((1+sintheta+icostheta)/(1+sintheta-icostheta))^n =cos((npi)...

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  7. If alpha "and" beta "are roots "x^2-2x+4=0 "then show that"alpha^n+bet...

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  8. For a positive integer n show that (1+i)^n+(1-i)^n=2^((n+2)/2) "cos((n...

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  9. For a positive integer n show that (1+isqrt3)^n+(1-isqrt3)^n=2^(n+1) "...

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  10. Letx+1/x=2cos alpha, y+1/y=2cos beta z+1/z=2cosgamma."Show that"2 "co...

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  11. Letx+1/x=2cos alpha, y+1/y=2cos beta z+1/z=2cosgamma."Show that"2 "co...

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  12. Solve x^9+x^5-x^4=1

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  13. Find the general value of theta" if"(cos theta+isintheta)("cos"2theta+...

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  14. If z=x+iy"show that" |x|+|y|lesqrt2|z|

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  15. Show thatRe(z1z2)=Rez1Rez2-Im z1Imz2 Im(z1z2)=Re z1 Im z2+Re z2 Im z1

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  16. What is the value of arg omega+ arg omega^2?

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  17. If |z1|le1,|z2|le1"show that" |1-z1z2|^2-|z1-z2|^2=(1-|z1|^2)(1-|z2|^2...

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  18. If z1^2+z2^2+z3^2-z2z3-z3z4=0 Show that |z1-z2|=|z2-z3|=|z3-z1|

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  19. Solve ((1-i)x+3i)/(2+i)+((3+2i)y+i)/(2-i)=-i "where" x, y, in R.

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  20. Find the region on the Argand plane on which z satisfies1lt|z-2i|lt3

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