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A rectangle of maximum area is inscribed...

A rectangle of maximum area is inscribed in the circle `|z-3-4i|=1.` If one vertex of the rectangle is `4+4i ,` then another adjacent vertex of this rectangle can be `2+4i` b. `3+5i` c. `3+3i` d. `3-3i`

A

`2+ 4i`

B

`3+5i`

C

`3+3i`

D

`3-3i`

Text Solution

Verified by Experts

The correct Answer is:
B, C

Clearly ,the inscribed rectangle is a square. Let the adjacement vertex be. Then
`(3+4i -(z))/((3+ 4i)-(4+ 4i)) =e^(pmipi//2)` (by rotation about centre)
`rArr 3+ 4i-z = pm i(-1)`
`rArr z =3 + 4 i pm = 3 + 5i or 3+ 3i`
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CENGAGE-COMPLEX NUMBERS-Exercise (Multiple)
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  3. A rectangle of maximum area is inscribed in the circle |z-3-4i|=1. If ...

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  6. If arg(z+a) = pi//6 and arg(z-a) = 2 pi//3 (a in R^(+)), then

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  7. If a complex number z satisfies |z| = 1 and arg(z-1) = (2pi)/(3), then...

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  8. If |z-1|=1, then

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  9. If z(1) = 5 + 12i and |z(2)| = 4, then

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  10. Let z(1),z(2),z(3) be the three nonzero comple numbers such that z(2)...

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  12. If |(z-z(1))//(z-z(2))| = 3, where z(1) and z(2) are fixed complex ...

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  13. If z=x+i y , then he equation |(2z-i)//(z+1)|=m represents a circle, t...

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  15. Let the equaiton of a ray be |z-2|-|z-1-i| = sqrt(2). If the is stri...

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  19. If P andn Q are represented by the complex numbers z(1) and z(2) such...

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  20. Loucus of complex number satifying are arg[(z-5+4i)//(z+3-2i)] = - pi...

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