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If |z1/z2|=1 and arg (z1z2)=0 , then ...

If `|z_1/z_2|=1` and `arg (z_1z_2)=0` , then a. `z_1 = z_2` b. `|z_2|^2 = z_1*z_2` `c. z_1*z_2 = 1` d. none of these

A

`z_(1) = z_(2)`

B

`|z_(2)|^(2) = z_(1)z_(2)`

C

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

D

more than 8

Text Solution

Verified by Experts

The correct Answer is:
B
Let `z_(1)=|z_(1)|(costheta_(1)+I sintheta_(1))`.
Now, `|(z_(1))/(z_(2))|=1rArr|z_(1)|=|z_(2)|`
Also, `arg(z_(1)z_(2))=0orarg(z_(1)+arg(z_(2))=0`
`rArr arg(z_(2))=-theta_(1)`
`rArr z_(2)=|z_(2)|(cos(-theta_(1))+i sin(-theta_(1)))`
`=|z_(1)|(costheta_(1)-isintheta_(1))=barz_(1)`
`rArr |z_(2)|=bar((barz_(1)))=z_(1)`
`rArr|z_(2)|^(2)=z_(1)z_(2)`
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