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Prove that the complex numbers `z_1 and z_2` and the origin form an isosceles triangle with vertical angle `2pi//3" if " z_1^2+z_2^2+z_1z_2=0`

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Prove that the complex numbers z_(1) and z_(2) and the origin form an isosceles triangle with vertical angle (2pi)/(3),ifz_(1)^(2)+z_(2)^(2)+z_(1)z_(2)=0.

The complex numbers z_(1) and z_(2) and the origin form an isosceles trangle with vertical angle (2 pi)/(3), then a.z_(1)^(2)+z_(2)^(2)=z_(1)z_(2)bz_(1)^(2)+z_(2)^(2)+z_(1)z_(2)=0c*z_(1)^(2)+z_(2)^(2)=3z_(1)z_(2)d none of these

Prove that the complex numbers z_(1),z_(2) and the origin form an equilateral triangle only if z_(1)^(2) + z_(2)^(2) - z_(1)z_(2)=0 .

The complex numbers z_1, z_2 and the origin form an equilateral triangle only if (A) z_1^2+z_2^2-z_1z_2=0 (B) z_1+z_2=z_1z_2 (C) z_1^2-z_2^2=z_1z_2 (D) none of these

Complex numbers z_1 , z_2, z_3 are the vertices A, B, C respectively of an isosceles right angled triangle with right angle at C. Show that (z_1-z_2)^2 =2 (z_1 - z_3) (z_3-z_2) .

MOTION-COMPLEX NUMBER -EXERCISE - 3 (LEVEL -III) SUBJECTIVE - JEE ADVANCED
  1. If O is origin and affixes of P, Q, R are respectively z, iz, z + iz. ...

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  2. If O is origin and affixes of P, Q, R are respectively z, iz, z + iz. ...

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  3. The region represented by RE(z)<=2, Im(z)<=2 and pi/8<=arg(z)<=(3pi)/8...

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  4. Let I Arg((z-8i)/(z+6))=pmpi/2 II: Re ((z-8i)/(z+6))=0 Show that ...

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  5. if a and bbetween 0 and 1 such that the points (a, 1). (1, b) and (0, ...

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  6. Find the non-zero complex numbers z satisfying z =i z^2dot

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  7. If the complex numbers z1, z2,.......zn lie on te unit circle |z| = 1 ...

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  8. Find the Cartesian equations of the locus of z in the complex plane sa...

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  9. Prove that the complex numbers z1 and z2 and the origin form an isosce...

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  10. If the complex number P(w) lies on the standard unit circle in an Arg...

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  11. Let z=x+i y be a complex number, where xa n dy are real numbers. Let A...

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  12. For all real numbers x, let the mapping f (x) = 1/(x-i). where i =sqrt...

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  13. Given that |z-1|=1, where z is a point on the argand planne , show...

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  14. Dividing f(z) by z- i, we obtain the remainder i and dividing it by z...

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  15. If the equation x^4+ax^3+bx^2+cx+d=0 has four imaginary roots two with...

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  16. If z1, z2 are the roots of the equation az^2 + bz + c = 0, with a, b, ...

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  17. Find the set of points on the argand plane for which the real part of ...

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  18. The equation z^n – 1 = 0 has n roots which are called the nth roots o...

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  19. The equation z^n – 1 = 0 has n roots which are called the nth roots o...

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  20. MATCH THE COLUMN {:(Column-I,Column-II),("(A) If "|ai|lt1,lamda1ge0 ...

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