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If z1,z2,z3 are complex numbers such tha...

If `z_1,z_2,z_3` are complex numbers such that `2/z_1=1/z_2 + 1/z_3`, show that the points represented by `z_1,z_2,z_3` lie on a circle passing through the origin.

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PATHFINDER-COMPLEX NUMBER-QUESTION BANK
  1. Find the centre and radius of circle 2absz^2+(3-i)z +(3+i)barz-7=0

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  2. Find all the circles which are orthogonal to absz=1 and abs(z-1)=4

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  3. If z1,z2,z3 are complex numbers such that 2/z1=1/z2 + 1/z3, show that ...

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  4. If 4x+i(3x-y)=3+i(-6), where x and y are real numbers, then find the v...

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  5. Find the multiplicative inverse of 2-3i.

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  6. Convert the complex number (-16)/(1+isqrt3) into polar form.

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  7. Find real theta such that (3+2isintheta)/(1-2isintheta) is purely real...

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  8. Convert the complex number z=(i-1)/(cos(pi/3)+isin(pi/3)) in the polar...

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  9. {1+(-i)^(4n+3)}(1-i), (ninN) equals

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  10. If z1,z2 are conjugate complex numbers and z3,z4 are also conjugate, t...

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  11. If z=(1+i)(1+sqrt 3i)^2/(1-i), then argz equal

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  12. The equation z^3=barz has

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  13. In the argand plane ABCD is a square described in the anticlockwise se...

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  14. (-64)^(1/4) equals

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  15. If omega is an imaginary cube root of unity then the value of omega^n+...

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  16. Solve: z^7-1=0

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  17. Located the complex numbers z=x+iy for which: log(1/2)((abs(z-1)+4)/(3...

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

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  19. Express the following expreeion in the form of a+ib : ((3+isqrt5)(3-is...

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  20. If z1=2-i, z2=1+i, find abs((z1+z2+1)/(z1-z2+i))

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