1.

If z_1 andz_2are two non- zero comlex numbers such that |z_1+z_2|=|z_1|+|z_2| then arg (z_1)- arg (z_2) is equal to

Answer»

`-pi`
`-pi/2`
0
`pi/2`

Solution :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|`
` rArr2|z_1||z_2|cos (arg z_1-arg z_2)=2|z_1|z_2|`
`rArrcos(arg z_1 - arg z_2)=1`
`rArrarg(z_1)aargz_2)=0`


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