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Show that if iz^3+z^2-z+i=0, then |z|=1...

Show that if `iz^3+z^2-z+i=0`, then `|z|=1`

A

Re z = 0

B

Im z = 0

C

|z| = 1

D

None of these

Text Solution

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The correct Answer is:
C
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MCGROW HILL PUBLICATION-COMPLEX NUMBERS -EXERCISE LEVEL 1
  1. Let omega = - (1)/(2) + i (sqrt3)/(2), then the value of the determina...

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  2. The inequality |z-i| lt |z + i| represents the region

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  3. Show that if iz^3+z^2-z+i=0, then |z|=1

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  4. If x + iy = (1)/(1-cos theta + 2 i sin theta), theta ne 2n pi, n in I,...

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  5. The equation z^3=bar z has

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  6. If z = 5 + t + isqrt(25 - t^(2)), (-5 le t le 5), then locus of z is a...

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  7. If omega is complex cube root of that 1/(a+omega)+1/(b+omega)+1/(c+ome...

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  8. if |z-iRe(z)|=|z-Im(z)| where i=sqrt(-1) then z lies on

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  9. If omega is a complex cube root of unity, then value of expression cos...

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  10. If roots of the equation z^2+ az + b = 0 are purely imaginary then

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  11. The system of equations |z+1-i|=sqrt2 and |z| = 3 has

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  12. If 8iotaz^3+12z^2-18z+27iota=0 then: a. |z|=3/2 b. |z|=2/3 c. |z|=...

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  13. If a complex number z lies in the interior or on the boundary of a cir...

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  14. If x+iy=3/(2+costheta +i sin theta), then show that x^2+y^2=4x-3

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  15. Suppose z(1), z(2), z(3) represent the vertices A, B and C respectivel...

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  16. Suppose that three points z(1), z(2), z(3) are connected by the relati...

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  17. If the number (z-1)/(z+1) is purely imaginary, then

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  18. If z s a complex number such that -pi/2 leq arg z leq pi/2, then which...

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  19. If |omega|=1, then the set of points z=omega+1/omega is contained in o...

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  20. The number of complex numbers z such that |z|=1a n d|z// z + z //z=1...

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