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If arg(z) < 0 then arg(-z)-arg(z)= (1) p...

If `arg(z) < 0` then `arg(-z)-arg(z)=` (1) `pi` (2) `-pi` (3) `- pi/2` (4) `pi/2`

A

`pi`

B

`-pi`

C

`- pi//2`

D

`pi //2`

Text Solution

Verified by Experts

The correct Answer is:
A
Since arg (z) `lt 0 rArr arg (z) =-theta`

`rArr z=r cos (- theta )`
`=r (cos theta - I sin theta)`
`-z = -r [ cos (pi - theta)+ I sin (pi - theta )]`
`therefore arg (-z) = pi - theta`
Thus ,arg (-z)-arg (z)
`= pi - theta - (- theta)=pi`
Alternate Solution
Reason arg (-z)-arg `((-z)/(z)) = arg (-1) =pi `
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