Complex NumbersHard
Question
If z = (3 + 7i) (p + iq), where p, q ∈ I - {0}, is purely imaginary, then minimum value of |z|2 is
Options
A.0
B.58
C.
D.3364
Solution
z = (3p - 7q) + (7p + 3q) i
∵ z is purely imaginary
3p = 7q
p = 7 q = 3 for minimum value of |z|2
|z|2 = 58 × 58
= 3364
∵ z is purely imaginary
3p = 7q
p = 7 q = 3 for minimum value of |z|2
|z|2 = 58 × 58
= 3364
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