If \( \mathrm{z} \) is any complex number satisfying \( |\mathrm{z}-\mathrm{k}|=\mathrm{k} \), w...
If \( \mathrm{z} \) is any complex number satisfying \( |\mathrm{z}-\mathrm{k}|=\mathrm{k} \), where \( \mathrm{k} \) is +ve real number, then which of the following is correct?
Column-I
(A) \( 2 \arg z \)
(B) \( |z|_{\max } \)
(C) \( (\arg z)_{\max } \) tends to
(a) \( \mathrm{A} \rightarrow \mathrm{q} ; \mathrm{B} \rightarrow \mathrm{s} ; \mathrm{C} \rightarrow \mathrm{p} \)
(b) \( \mathrm{A} \rightarrow \mathrm{r} ; \mathrm{B} \rightarrow \mathrm{s} \); C \( \rightarrow \mathrm{q} \)
(c) \( \mathrm{A} \rightarrow \mathrm{q} ; \mathrm{B} \rightarrow \mathrm{p} ; \mathrm{C} \rightarrow \mathrm{r} \)
(d) \( \mathrm{A} \rightarrow \mathrm{s} ; \mathrm{B} \rightarrow \mathrm{p} ; \mathrm{C} \rightarrow \mathrm{r} \)
Column-II
(p) \( \pi / 2 \)
(q) \( \arg (z-k) \)
(r) \( \arg (z+k) \)
(s) \( 2 k \)
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