JEE Mains · Maths · STD 11 - 4.1 complex nubers
If for the complex numbers \(z\) satisfying \(|z-2-2 i| \leq 1\), the maximum value of \(|3 i z+6|\) is attained at \(\mathrm{a}+i \mathrm{~b}\), then \(\mathrm{a}+\mathrm{b}\) is equal to .... .
- A \(3\)
- B \(4\)
- C \(5\)
- D \(6\)
Answer & Solution
Correct Answer
(C) \(5\)
Step-by-step Solution
Detailed explanation
\(|z-2-2 i| \leq 1\) \(|x+i y-2-2 i| \leq 1\) \(|(x-2)+i(y-2)| \leq 1\) \((x-2)^{2}+(y-2)^{2} \leq 1\) \(\mid3 i z+\left.6\right|_{\max } \text { at } a+i b\) \(\mid3 i|| z+\frac{6}{3 i} \mid\) \(3|z-2 i|_{\max }\) From Figure maximum distance at \(3+2 \mathrm{i}\)…
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