if z=(3+7i)(p+iq),where p,q are non-zero integers,is purely imaginary then minimum value of |z|^2 is

3364
  • -15

z=(3+7i) (p+iq)=(3p-7q)+i(3q+7p)
now it is said z is purely imaginary
so,
3p-7q=0
or p/q=7/3
or p/q + i = 7/3 +i
(p+qi)/q=7+3i/3
from here the p+iq = 7+3i

z= 58i
|z2|= 3364

  • 7
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