Saved Bookmarks
| 1. |
If|z _1 |= 2and(1-i)z_2+(1+i)barz_2= 8sqrt2, then the minimumvalue of|z_1 - z_2| is ______. |
|
Answer» Thisimplies that `z_(1)` lies on the circlehaving centre at origin and radius 2. `(1-i) z_(2) +(1+i) barz_(2) = 8sqrt(2)` `THEREFORE (1-i)(x_(2) + iy_(2)) +(1+i)(x_(2) -iy_(2)) = 8sqrt(2)` `rArr x_(2)+y_(2) = 4sqrt(2)` So, `z_(2)` lies on thestraightline ` + y = 4sqrt(2)` ![]() `|z_(1) -z_(2)|_("min")=` shortest distance betweencircleand straightline = AB `= OB - OA` `= 4- 2=2` |
|