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Show that the complex numbers `z_(1),z_(2),z_(3)` satisfying `(z_(1)-z_(3))/(z_(2)-z_(3))=(1-sqrt(3))/(2)` are the verticels of an equilaterla triangle.

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In the complex plane, the vertices of an equlitateral triangle are represented by the complex numbers z_(1),z_(2) and z_(3) prove that, (1)/(z_(1)-z_(2))+(1)/(z_(2)-z_(3))+(1)/(z_(3)-z_(1))=0

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CHHAYA PUBLICATION-MISCELLANEOUS EXAMPLES-ALGEBRA
  1. Obtain the sum of (1)/(x+1)+(2)/(x^(2)+1)+(4)/(x^(4)+1)+...+ (2^(n))/(...

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  2. Let A and B be two comoplex numbers such that (A)/(B)+(B)/(A)=1. Prove...

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  3. Show that the complex numbers z(1),z(2),z(3) satisfying (z(1)-z(3))/(z...

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  4. If z(1),z(2),z(3) are complex numbers such that |z(1)|=|z(2)|=|Z(3)|=|...

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  5. Show that (666 ...n "times")^(2)+(888.... N times) =(444.... 2n times)...

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  6. Let z(1)=10+6i and z(2)=4+6i. If z is complex number such that the arg...

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  7. z(1) and z(2) are two non-zero complex numbers, they form an equilater...

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  8. If the complex numbers z(1),z(2),z(3) represents the vertices of an e...

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  9. If omega is an imaginary cube root of unity. Find the value of the exp...

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  10. Find the sum of all multiples 3 or 4 between 1 and 325.

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  11. The vertices A,B,C of an isosceles right angled triangle with right an...

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  12. If n ge0 is integer, using induction method prove that, (1)/(1+x)+(2...

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  13. Find the differential coefficient of: x^(5x)

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  14. If x+y=a+b and x^(2)+y^(2)=a^(2)+b^(2), then by mathematical induction...

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  15. By the principle of mathematical induction prove that, (2^(2^(n))+1) h...

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  16. Find the differential coefficient of: x^(9)-5x^(2)+3x

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  17. Find the solution set of inequation (x-2)/(x+5) gt2.

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  18. Find the differential coefficient of: x^(5)+4x

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  19. Find the differential coefficient of: x^(2x)

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  20. Using mathematical induction prove that, "tan"^(-1)(x)/(1*2+x^(2))+"...

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