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LetA (z_1 )andB(z_2 )be lying onthe curve|z-3 - 4i| = 5, where|z_1 |is maximum. Now,A(z_1) is rotated about the origin inanticlockwise direction through 90^(@)reachingatP(z_0). IfA, B and Pare collinear thenthevalue of(|z_0 - z_ 1 | * |z_ 0- z_ 2 |)is _______. |
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Answer» So, z lies on the circlehaving centre at `3+4i` and radius 5. This circlepasses thorughtthe origin. `z_(1)` lies on circlesuch that `|z_(1)|` is MAXIMUM. Therefore ,`z_(1) ` is at other end of thediameter through origin. `therefore z_(1) = 6+ 8i` OAis rotated by `90^(@)` in anticlcokwise DIRECTION. So, `z_(0) = i(6+8i) = - 8+ 6i` Since A,B and P are colliner. `|z_(0)-z_(1)|.|z_(0)-z_(2)| = Pa.PB =OP^(2) = 10^(2) = 100` |
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