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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

58

D

65

Text Solution

Verified by Experts

The correct Answer is:
C
`z=(3a-7b)+i(3b+7a)`
For z to be purely imaginary, we have
`3a=7b`
`rArra =7 or b=3` (for least value of `|z|`)
`rArr |z| =|3+7i|`
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