1.

If `z_1` and `z_2` are two non- zero comlex numbers such that `|z_1+z_2|=|z_1|+|z_2|` then arg `(z_1)- arg (z_2)` is equal toA. `-pi`B. `-pi/2`C. 0D. `pi/2`

Answer» Correct Answer - C
Given `|z_1+z_2|=|z_1|+|z_2|`
On squaring both sides ,we get
`|z_1|^2 + |Z_2|^2+2|z_1||z_2|cos (arg z_1 - arg z_2)=|z_1|^2|z_2|^2+2|z_1||z_2|`
` rArr 2|z_1||z_2|cos (arg z_1-arg z_2)=2|z_1|z_2|`
`rArr cos(arg z_1 - arg z_2)=1`
`rArr arg(z_1)aargz_2)=0`


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