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If a m p(z1z2)=0a n d|z1|=|z2|=1,t h e n...

If `a m p(z_1z_2)=0a n d|z_1|=|z_2|=1,t h e n` `z_1+z_2=0` b. `z_1z_2=1` c. `z_1=z _2` d. none of these

A

`z_(1)+z_(2) = 0`

B

`z_(1)z_(2) = 1`

C

`z_(1)=barz_(2)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B, C
`amp(z_(1)z_(2)) = 0`
` rArr amp z_(1) + ampz_(2) = 0`
` therefore amp z_(1) + amp z_(2) = amp barz_(2)`
Since `|z_(1)| = |z_(2)|`, we get `|z_(1)| = |barz_(1)|`.
So, `z_(1) = barz_(2)`. Also, `barz_(1)z_(2) = barz_(2)z_(2) = |z_(2)|^(2) = 1` because `|z_(2)|=1`
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