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If for complex numbers z1 and z2, arg(z...

If for complex numbers `z_1 and z_2, arg(z_1) -arg(z_2)=0` then `|z_1-z_2|` is equal to

A

`|z_(1)|+|z_(2)|`

B

`|z_(1)| - |z_(2)|`

C

`||z_(1)|-|z_(2)||`

D

0

Text Solution

Verified by Experts

The correct Answer is:
C
We have
`|z_(1)-z_(2)|^(2)=|z_(1)|^(2)+|z_(2)|^(2)-2|z_(1)||z_(2)|cos(theta_(1)-theta_(2))`
where `theta_(1)=arg(z_(1))and theta_(2)=arg(z_(2))`. Given,
`arg(z_(1))-arg(z_(2))=0`
`rArr|z_(1)-z_(2)|^(2)=|z_(1)|^(2)+|z_(2)|^(2)-2|z_(1)||z_(2)|`
`=(|z_(1)|-|z_(2)|)^(2)`
`rArr|z_(1)-z_(2)|=||z_(1)|-|z_(2)||`
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