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Prove that the triangle formed by the po...

Prove that the triangle formed by the points `1,(1+i)/(sqrt(2)),a n di` as vertices in the Argand diagram is isosceles.

A

scalene

B

equilateral

C

isosceles

D

right-angled

Text Solution

Verified by Experts

The correct Answer is:
c
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OBJECTIVE RD SHARMA-COMPLEX NUMBERS -Chapter Test
  1. If n1, n2 are positive integers, then (1 + i)^(n1) + ( 1 + i^3)^(n1) +...

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  2. The modulus of sqrt(2i)-sqrt(-2i) is

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  3. Prove that the triangle formed by the points 1,(1+i)/(sqrt(2)),a n di ...

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  4. The value of (1+isqrt(3))/(1-isqrt(3))^(6)+(1-isqrt(3))/(1+isqrt(3))^(...

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  5. If alpha+ibeta=tan^(-1) (z), z=x+iy and alpha is constant, the locus o...

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  6. If cosA+cosB+cosC=0,sinA + sinB + sinC=0and A+B+C=180^0, then the valu...

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  7. The value of the expression 1.(2-omega).(2-omega^2)+2.(3-omega)(3-omeg...

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  8. The value of the expression (1+1/omega)(1+1/omega^(2))+(2+1/omega)(2+...

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  9. The condition that x^(n+1)-x^(n)+1 shall be divisible by x^(2)-x+1 is ...

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  10. The expression (1+i)^(n1)+(1+i^(3))^(n(2)) is real iff

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  11. |{:("6i " "-3i " "1" ),("4 " " 3i" " -1"),("20 " "3 " " i"):}|=x+iy th...

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  12. The centre of a square ABCD is at z0dot If A is z1 , then the centroid...

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  13. If cosalpha+2cosbeta+3cosgamma=sinalpha+2sinbeta+3singamma=0 and alpha...

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  14. If cosalpha+2cosbeta+3cosgamma=sinalpha+2sinbeta+3singamma=0 and alpha...

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  15. Sum of the series sum(r=0)^n (-1)^r ^nCr[i^(5r)+i^(6r)+i^(7r)+i^(8r)] ...

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  16. If az(1)+bz(2)+cz(3)=0 for complex numbers z(1),z(2),z(3) and real num...

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  17. If 2z1-3z2 + z3=0, then z1, z2 and z3 are represented by

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  18. Re((z+4)/(2z-1)) = 1/2, then z is represented by a point lying on

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  19. The vertices of a square are z1,z2,z3 and z4 taken in the anticlockwis...

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  20. Let lambda in R . If the origin and the non-real roots of 2z^2+2z+lam...

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