JEE Mains · Maths · STD 11 - 4.1 complex nubers
Let z be the complex number satisfying \( |z-5|\le3 \) and having maximum positive principal argument. Then \( 34|\frac{5z-12}{5iz+16}|^{2} \) is equal to :
- A 16
- B 12
- C 26
- D 20
Answer & Solution
Correct Answer
(D) 20
Step-by-step Solution
Detailed explanation
\( |z-5|\le3 \) For arg(z) to be maximum, z lies at P. \( z\equiv(4cos~\theta,4~sin~\theta) \) \( =(4\cdot(\frac{4}{5}),4(\frac{3}{5}))=(\frac{16}{5},\frac{12}{5})=\frac{16}{5}+\frac{12i}{5} \) Now, \( 34|\frac{5z-12}{5iz+16}|^{2}=34|\frac{(16+12i)-12}{(16i-12)+16}|^{2} \)…
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