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CBSE Class 11-science Answered

If z lies on the circle |z-1| = 1, then fraction numerator z minus 2 over denominator z end fraction is  purely real purely imaginary positive real none of these
Asked by akashkumar42620 | 04 May, 2019, 09:46: AM
answered-by-expert Expert Answer
z space l i e s space o n space t h e space c i r c l e space vertical line z minus 1 vertical line equals 1 space i. e. space a space c i r c l e space w i t h space c e n t r e space left parenthesis 1 comma 0 right parenthesis space a n d space r a d i u s space 1 S i n c e space z element of space vertical line z minus 1 vertical line equals 1 rightwards double arrow space vertical line z minus 1 vertical line equals 1 rightwards double arrow space z minus 1 equals 1 space o r space z minus 1 equals negative 1 rightwards double arrow z minus 2 equals 0 space o r space z equals 0 I f space z equals 0 comma space t h e n space t h e space v a l u e space o f space fraction numerator z minus 2 over denominator z end fraction space i s space n o t space d e f i n e d T h e r e f o r e comma space z minus 2 equals 0 rightwards double arrow space fraction numerator z minus 2 over denominator z end fraction equals 0 H e n c e comma space space fraction numerator z minus 2 over denominator z end fraction space i s space p u r e l y space r e a l.
Answered by Renu Varma | 05 May, 2019, 04:08: PM

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