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If z=3/(2+costheta+isintheta) then show ...

If `z=3/(2+costheta+isintheta)` then show that z lies on a circle in the complex plane

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If z be complex no. and (z-1)/(z+1) be purely imaginary show that z lies on the circle whose centre is at origin and the radius is 1

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PATHFINDER-COMPLEX NUMBERS-QUESTION BANK
  1. If omega is the imaginary cube root of 1 then prove that (a+bomega+com...

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  2. If y=sqrt(x^2+6x+8) then show that one of the value of sqrt(1+iy)+sqrt...

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  3. If x=cosalpha+isinalpha and 1+sqrt(1-y^2)=ny then show that y/2n(1+nx)...

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  4. If a=1/2(5-isqrt3) then find the value of a^3-6a^2+12a-8

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  5. Show that complex numbers (2+i3), (2-i3), (3-i2), (3+i2) are concyclic...

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  6. If in argand plane the vertices A,B,C of an isoceles triangle are rep...

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  7. If z1,z2,z3 are three complex number then prove that z1Im(barz2.z3)+z2...

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  8. Prove that (1-omega^2)(1-omega^2+omega^4)(1-omega^4+omega^8)………..to 2n...

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  9. If x-iy = sqrt((a+ib)/(c-id)), prove that (x^(2) + y^(2))^(2) = (a^(2)...

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  10. If z be complex no. and (z-1)/(z+1) be purely imaginary show that z li...

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  11. z1 and z2 be two complex no. then prove that abs(z1+z2)^2+abs(z1-z2)^2...

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  12. If z=3/(2+costheta+isintheta) then show that z lies on a circle in the...

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  13. If a=cosalpha+isinalpha , b=cosbeta+isinbeta , c=cosgamma+isingamma an...

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  14. Ifomega is the imaginary cube root of unity and a+b+c=0 then show that...

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  15. Ifz1,z2,z3 represent three vertices of an equilateral triangle in arga...

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  16. Prove that the complex numbers z1,z2 and the origin from an isoceles t...

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  17. If (1+x)^n=a0+a1x+a2x^2+…..+anx^n then show that (a0-a2+a4-……)^2+(a1-a...

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  18. If z1,z2,z3………..zn are n complex numbers s.t, abs(z1)=abs(z2)=………….abs...

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  19. z1 and z2 be two complex no. then prove that abs(z1+z2)^2+abs(z1-z2)^2...

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  20. If costheta=1/2(a+1/a) cos(phi)=1/2(b+1/b) show that one of the valu...

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