Mathematics

LIKE TO JOIN ON FACEBOOK ( click here ) 1. If    then find the complex no. for which | z - 1 | is least and maximum and find the least and maximum value of | z - 1| Sol. Since   represent a region under the circle of radius 1 and centre at (0,1). It also includes the perimetre of the circle, | z - 1 | can also equal to 1 We have to find the least and Max value of | z - 1 |, | z - 1 | is the distance between the complex no. 1 and z. Since 'z' belongs to the region under the circle. so we have to find that point on the region which is at the least distance from the point (1,0) i.e. complex no. 1 + 0i By, geometry AP is the least distance from the region of disk and BP is the maximum distance. Therefore,                                                           = CP - CA                                                        (    )   And,                              = CP + BC                              Further we have to find the complex

LIKE TO JOIN ON FACEBOOK ( click here ) 13.    z = x + iy then,  14.  if z = x + iy 1/z = 1/ (x + iy)                     since,  therefore,  or,   is the equation of circle having centre (0,1) and radius '1'. The region represented of   is outside of the circle. , radius = 1 NOTE:  = distance between   &   . 1. | z + i | = | z - i | i.e. | z + i | = | z - (-i ) | distance of z from '-i'  and | z - i | = distance of z from 'i'  Therefore, locus of 'z' is the perpendicular bisector of the line joining 'i' and '-i' 2. | z + 2 - 3i | = | z - 3 + i | | z + 2 - 3i | = distance of z from -2 + 3i  | z - 3 + i | = distance of z from 3 - i locus of z is the perpendicular bisector of line joining (-2,3) and (3,-1) 3. | z - i | = 1 distance of z from i = 1 ( constant) therefore the equation represents circle  , Radius = 1 Equation in coordinate form: 4. 1 < | z