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In argand plane |z| represent the distan...

In argand plane `|z|` represent the distance of a point z from the origin. In general `|z_(1)-z_(2)|` represent the distance between two points `z_(1)` and `z_(2)`. Also for a general moving point z in argand plane, if `arg(z)=theta`, then `z=|z|e^(i theta)`, where `e^(i theta)=cos theta+i sin theta`.
If `|z-(3+2i)|=|z cos((pi)/(4)-"arg z")|`, then locus of z is

A

circle

B

parabola

C

ellipse

D

hyperbola

Text Solution

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The correct Answer is:
B
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Knowledge Check

  • Read the following writeup carefully: In argand plane |z| represent the distance of a point z from the origin. In general |z_1-z_2| represent the distance between two points z_1 and z_2 . Also for a general moving point z in argand plane, if arg(z) =theta , then z=|z|e^(itheta) , where e^(itheta) = cos theta + i sintheta . Now answer the following question If |z-(3+2i)|=|z cos ((pi)/(4) - "arg" z)|, then locus of z is

    A
    circle
    B
    parabola
    C
    ellipse
    D
    hyperbola

  • In argand plane |z| represent the distance of a point z from the origin. In general |z_(1)-z_(2)| represent the distance between two points z_(1) and z_(2) . Also for a general moving point z in argand plane, if arg(z)=theta , then z=|z|e^(i theta) , where e^(i theta)=cos theta+i sin theta . If z_(1)=4e^(i pi//3) and z_(2)=2e^(i5pi//6) , then |z_(1)-z_(2)| equals

    A
    20
    B
    `2sqrt(3)`
    C
    `sqrt(20)`
    D
    `20sqrt(3)`

  • Read the following writeup carefully: In argand plane |z| represent the distance of a point z from the origin. In general |z_1-z_2| represent the distance between two points z_1 and z_2 . Also for a general moving point z in argand plane, if arg(z) =theta , then z=|z|e^(itheta) , where e^(itheta) = cos theta + i sintheta . Now answer the following question [|z-z_1|-|z-z_2|]=t , where t is real parameter always represents

    A
    ellipse
    B
    hyperbola
    C
    circle
    D
    None of these

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