JEE Mains · Maths · STD 11 - 4.1 complex nubers
Let z be a complex number such that \(|z-6|=5\) and \(|z+2-6i|=5\). Then the value of \(z^{3}+3z^{2}-15z+141\) is equal to
- A 42
- B 37
- C 50
- D 61
Answer & Solution
Correct Answer
(C) 50
Step-by-step Solution
Detailed explanation
Center of first circle \(C_{1}(6,0), r_{1}=5\) Center of second circle \(C_{2}(-2,6), r_{2}=5\) \(\because C _1 C _2= r _1+ r _2\) \(\therefore\) common point Z is mid point of \(C_{1}\) & \(C_{2}\) \(\therefore\) \(z=2+3i\) \(\therefore\) \(z^{2}=4z-13\) \(\therefore\)…
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