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If z=(3+7i)(a+ib), where a, b in Z-{0}, ...

If `z=(3+7i)(a+ib)`, where `a`, `b in Z-{0}`, is purely imaginery, then minimum value of `|z|^(2)` is

A

`74`

B

`45`

C

`65`

D

`58`

Text Solution

Verified by Experts

The correct Answer is:
D
`(d)` `z=(3a-7b)+i(3b+7a)`
For purely imaginary, `3a=7b`
`impliesa=7` or `b=3` (for least value of `|z|`)
`implies |z|=|3+7i|=sqrt(58)`
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