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Let Z(1) and Z(2) be two complex numbers...

Let `Z_(1)` and `Z_(2)` be two complex numbers satisfying `|Z_(1)|=9` and `|Z_(2)-3-4i|=4`. Then the minimum value of `|Z_(1)-Z_(2)|` is

A

`|Z_(4)|=1`

B

`arg(Z_(1)Z_(4))=-pi//2`

C

`(Z_(5))/(cos(argZ_(1)))+(Z_(6))/(sin(argZ_(1)))` is purely real

D

`Z_(5)^(2)+(barZ_(6))^(2)` is purely imaginergy

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D

`(a,b,c,d)` `Z_(1)=e^(itheta_(1))`, `Z_(2)=e^(itheta_(2))`, `Re(Z_(1)Z_(2))=0impliestheta_(1)+theta_(2)=-pi//2`, (as `z_(1)`, `z_(2)` lie in fourth quadrant)
`Z_(3)=e^(-itheta_(1))`, `Z_(4)=-e^(itheta_(1))`, `Z_(5)=costheta_(1)(1-i)`, `Z_(6)=sintheta_(1)(-1+i)`
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