`z_(1)`, `z_(2)` are two distinct points in complex plane such that `2|z_(1)|=3|z_(2)|` and `z in C` be any point `z=(2z_(1))/(3z_(2))+(3z_(2))/(2z_(1))` such that

Options

A. `-1 le Re z le 1`
B. `-2 le Re z le 2`
C. `-3 le Re z le 3`
D. None of these

Answer

B

Explanation

`(b)` `z=(2z_(1))/(3z_(2))+(3z_(2))/(2z_(1))`
`=(2)/(3)(|z_(1)|)/(|z_(2)|)e^(i(theta_(1)-theta_(2)))+(3)/(2)(|z_(2)|)/(|z_(1)|)e^(i(theta_(2)-theta_(1)))`
`=e^(i(theta_(1)-theta_(2)))+e^(i(theta_(2)-theta_(1)))=2cos(theta_(1)-theta_(2))=2cosalpha`