12th sum

Asked by lovemaan5500 | 9th Oct, 2018, 06:39: AM

Expert Answer:

1. space vertical line z minus 2 vertical line equals 2 vertical line z plus 2 vertical line

l e t space z equals space x plus i y
vertical line x plus i y minus 2 vertical line equals 2 vertical line x plus i y plus 2 vertical line
vertical line x minus 2 plus i y vertical line equals 2 vertical line x plus 2 plus i y vertical line
square root of left parenthesis x minus 2 right parenthesis squared plus y squared end root equals 2 square root of left parenthesis x plus 2 right parenthesis squared plus y squared end root
t a k i n g space s q u a r e space t o space b o t h space s i d e
w e space g e t space
left parenthesis x minus 2 right parenthesis squared plus y squared equals 4 left square bracket left parenthesis x plus 2 right parenthesis squared plus y squared right square bracket
left parenthesis x minus 2 right parenthesis squared plus y squared equals 4 left parenthesis x plus 2 right parenthesis squared plus 4 y squared
x squared minus 4 x plus 4 plus y squared equals 4 x squared plus 16 x plus 16 plus 4 y squared
3 x squared plus 20 x plus 12 plus 3 y squared equals 0
3 left parenthesis x squared plus 20 over 3 x plus 4 plus y squared right parenthesis equals 0
x squared plus 20 over 3 x plus 4 plus y squared equals 0
x squared plus 20 over 3 x plus 100 over 9 plus 4 minus 100 over 9 plus y squared equals 0
left parenthesis x plus 10 over 3 right parenthesis squared plus y squared equals 64 over 9

b a s i c a l l y space i t space i s space c i r c l e space w i t h space c e n t r e space left parenthesis negative 10 over 3 comma 0 right parenthesis space r a d i u s space 8 over 3 space.

2. space vertical line z minus 2 i vertical line equals 1
l e t space z equals x plus i y
vertical line x plus i y minus 2 i vertical line equals 1
vertical line x plus i left parenthesis y minus 2 right parenthesis vertical line equals 1
x squared plus left parenthesis y minus 2 right parenthesis squared equals 1
b a s i c a l l y space i t space i s space c i r c l e space w i t h space c e n t r e space left parenthesis 0 comma 2 right parenthesis space r a d i u s space 1 space.

Answered by Ram Singh | 18th Oct, 2018, 08:16: PM