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If z and w are two complex number such t...

If `z and w` are two complex number such that `|zw|=1 and arg (z) – arg (w) = pi/2,` then show that `overline zw = -i.`

A

`bar(z) w = -i`

B

`bar(z)w =i`

C

`z bar(w) = (-1 + i)/(sqrt2)`

D

`z bar(w) = (1 - i)/(sqrt2)`

Text Solution

Verified by Experts

The correct Answer is:
A
`|zw| =1`
arg `((z)/(w)) = (pi)/(2)`
arg `(bar(z)w) = - (pi)/(2)`
`bar(z) w = -i " as " |zw| =1`
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