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The greatest positive argument of comple...

The greatest positive argument of complex number satisfying `|z-4|=R e(z)` is `pi/3` b. `(2pi)/3` c.`pi/2` d. `pi/4`

A

`(pi)/(3)`

B

`(2pi)/(3)`

C

`(pi)/(2)`

D

`(pi)/(4)`

Text Solution

Verified by Experts

The correct Answer is:
D
`|z-4|=Re(z)`
`rArr sqrt((x-4)^(2)+y^(2)=x)`
or `x^(2)-8x+16+y^(2)=x^(2)`
or `y^(2)=8(x-2)`

The given represents the parabola with focus (4, 0) and the imaginary axis as the directirx. The two tangents from directrix are at right angle. Hence, greatest positive argument of z is `pi//4`.
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