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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)) .

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UNITED BOOK HOUSE-JADAVPUR VIDYAPITH-EXERCISE
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  2. tan25^@=a prove that (tan155^@-tan115^@)/(1+tan155^@.tan115^@)=(1-a^2)...

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  3. Prove that tan70^(@)=2tan50^(@)+tan20^(@).

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  4. a=(1+i)/sqrt2then a^6+a^4+a^2+1=?

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  5. x(x-3)=4,has two roots alphaand betathen alpha^2+beta^2=?

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  6. Find the area of the triangle formed by the straight lin x cosalpha+ys...

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  7. Straight line px-qy=r intercept the coordinate axis at the point (a,0)...

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  8. A relation R defined on the set of natural no as follows R={(x,y),x+5y...

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  9. cos(beta-gamma)+cos(gamma-alpha)+cos(alpha-beta)=-3/2 show that cosalp...

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  10. sintheta+sinphi=a,costheta+cosphi=bshow that tan((theta-phi)/2)=+-sqrt...

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  11. If cos theta=(acosphi+b)/(a+bcosphi)(theta,phiacute angle)show that ta...

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  12. In a triangle ABC if a cos^2(C/2)+c cos^2(A/2)=((3b)/2)show that sides...

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  13. If w be a imaginary cube root of uniyt and a+b+c=0 then show that (a+b...

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

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  15. If the equation x^2+px+qr=0and x^2+qx+pr=0(p!=q,r!=0)has same root the...

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  16. Prove that ^nPr=^(n-1)Pr+r^(n-1)P(r-1)(notation used are in their usua...

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  17. How many way will be made from the word JADAVPUR taking al the letters...

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  18. If a,b,c are in G.P and x,y are the arithmetic mean of a and b aand b,...

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  19. Sum of the reciprocal intercepts on the axes by a moving straight lin...

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  20. Distance of the straight line 4x+3y=5 cosalphaand 6x-8y=5 sinalphafrom...

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