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An equilateral triangle in the Argan pla...

An equilateral triangle in the Argan plane has vertix as `z_1`,`z_2`and `z_3`which are there complex no show that `1/(z_1-z_2)+1/(z_3-z_1)+1/(z_2-z_3)=0`

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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

If in argand plane the vertices A,B,C of an isoceles triangle are represented by the complex nos z_1 ,z_2, z_3 respectively where angleC=90^@ then show that (z_1-z_2)^2=2(z_1-z_3)(z_3-z_2)

If z_1 and z_2 are two complex no. st abs(z_1+z_2) = abs(z_1)+abs(z_2) then

If z_1,z_2,z_3 are three complex number then prove that z_1Im(barz_2.z_3)+z_2Im(barz_3.z_1)+z_3Im(barz_1.z_2)=0

If z_1,z_2,z_3 represent three vertices of an equilateral triangle in argand plane then show that 1/(z_1-z_2)+1/(z_2-z_3)+1/(z_3-z_1)=0

z_1 and z_2 be two complex no. then prove that abs(z_1+z_2)^2+abs(z_1-z_2)^2=2[abs(z_1)^2+abs(z_2)^2]

If the vertices of an equilateral triangle be represented by the complex numbers z_(1),z_(2),z_(3) on the Argand diagram, then prove that, z_(1)^(2)+z_(2)^(2)+z_(3)^(2)=z_(1)z_(2)+z_(2)z_(3)+z_(3)z_(1).

Let z_1 and z_2 are two complex nos s.t. abs(z_1) =abs(z_2)=1 then abs((z_1-z_2)/(1-z_1 barz_2)) is equal to

The vertices A,B,C of an isosceles right angled triangle with right angle at C are represented by the complex numbers z_(1) z_(2) and z_(3) respectively. Show that (z_(1)-z_(2))^(2)=2(z_(1)-z_(3))(z_(3)-z_(2)) .

If z_1,z_2 and z_3,z_4 are two pairs of conjugate complex numbers, then arg(z_1/z_4)+arg(z_2/z_3) equals

UNITED BOOK HOUSE-MODEL QUESTION PAPERS-SET 14-EXERCISE
  1. In /\ABCif1/(a+c)+1/(b+c)=3/(a+b+c),show that angleC=pi/3

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  2. Using mathematical induction, prove that 1/5n^5+1/3n^3+7n/15 is a natu...

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  3. An equilateral triangle in the Argan plane has vertix as z1,z2and z3wh...

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  4. How many arragements can be made out of the letters of the word FAILUR...

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  5. Calcualte the sum of the series :1+3/2+7/4+15/8+31/16+….+tn

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  6. The equation of three sides of a triangle are x + 2y - 5 = 0, x +y = 6...

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  7. Show that the area of the triangle formed by the lines y = m(1) x + c(...

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  8. Find the equation, centre, and radius of a circle which is passes thro...

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  9. By using section formula, show that the points .(1, 2, 3), (-2, 4, 2) ...

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  10. Evaluate lim(xrarrpi//4)(4sqrt2-(cosx+sinx)^5)/(1-sin2x)

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  11. If f(x)=sqrt2x-sqrt(2/x)+(4-x)/(4-x), find the value of f(2)

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  12. If 2x^3 + 5x = 0, where x is a real number, then x = 0’ examine the st...

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  13. ‘If for any real no x, x^3 + x = 0, then x =0’ prove this by the metho...

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  14. A,B,C and D are four mutually exclusive and exhuastive events. If the ...

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  15. Prove thatcos^2alpha+cos^2(120^@-alpha)+cos^2(120^@+alpha)=3/2

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  16. Prove that tan 70^@ = tan 20^@ + 2 tan 50^@.

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  17. Prove that with the help of mathemetical induction. 4+44+444+...upto n...

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  18. If the roots of the equation ax^2+bx+c=0 are alpha,betaand the roots ...

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  19. Draw the graph and find the common region of the following system of i...

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  20. Show that there are 136 ways of selecting 4 letters from the word EXAM...

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