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Letz_1, z_2 , z_3in Csuchthat|z_1 |= |z_2| =|z_3| =|z_1+z_2+ z _3|=4 . If|z_1 - z _2 |= | z _1+z _ 3 |andz_2nez_3, thenvaluesof|z_1+z_2 |* |z_1+z _ 3|is_____. |
Answer» So,orhtocentre of trinagle is `z_(1)+z_(2)+z_(3)|=4` Given that `|z_(1)-z_(2)|=|z_(1)-z_(3)|` `rArr AB = AC ` `therefore angle BAC = 90^(@)` (orthocentre is at vertex A) Thus, `|z_(1)+z_(2)|.|z_(1)+z_(3)| = |z_(4) -z_(3)||z_(4)-z_(2)| ` `= (AC)(AB)= (4sqrt(2))(4sqrt(2)) = 32` |
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