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Let z(1) and z(2) be any two non-zero co...

Let `z_(1)` and `z_(2)` be any two non-zero complex numbers such that `3|z_(1)|=2|z_(2)|. "If "z=(3z_(1))/(2z_(2)) + (2z_(2))/(3z_(1))`, then

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

Text Solution

Verified by Experts

The correct Answer is:
B
`(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`
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