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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 |
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Answer» `-pi` 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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