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The region of Argand diagram defined by ...

The region of Argand diagram defined by `|z – 1| + |z + 1| le 4` is

A

interior of an ellipse

B

exterior of a circle

C

interior and boundary of an ellipse

D

None of these

Text Solution

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The correct Answer is:
C
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The region of argand diagram defined by |z-1|+|z+1|<=4 (1) interior of an ellipse (2) exterior of a circle (3) interior and boundary of an ellipse (4) none of these

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Knowledge Check

  • The region of Argand diagram defined by | z - 1| + | z + 1| le 4 is

    A
    interior of an ellipse
    B
    exterior of a circle
    C
    interior and boundary of an ellipse
    D
    none of these

  • The region in the Argand diagram defined by |z-2i|+|z+2i| lt 5 is the ellipse with major axis along

    A
    the real axis
    B
    the imaginary axis
    C
    `y=x`
    D
    `y=-x`

  • Area of the triangle in the argand diagram formed by the complex number z, is z + iz, where is z = x + iy is

    A
    |z|
    B
    `|z|^(2)`
    C
    `2|z|^2`
    D
    `1/2|z|^2`

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    Show that the area of the triangle on the Argand diagram formed by the complex number z,iz and z+iz is (1)/(2)|z|^(2)

    The greatest value of | z + 1| if | z + 4 | le 3 is

    If P is the affix of z in the Argand diagram and P moves so that (z - i)/( z - 1) is always purely imaginary, then locus of z is

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