Let $u = \frac{{2z + i}}{{z - ki}},\,\,z = x + iy{\rm{ }}\,\,{\rm{and }}\,\,k > 0.$ if the curve represented by ${\mathop{\rm Re}\nolimits} (u) + {\mathop{\rm Im}\nolimits} (u) = 1$ intersects the Y-axis at the point $P{\rm{ }}\,{\rm{and}}\,{\rm{ Q}}$ where $PQ=5$ then the value of k is

JEE MATHEMATICS MCQ: COMPLEX NUMBERS

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Analyzing +4 | -1

Let

u = \frac{{2z + i}}{{z - ki}},\,\,z = x + iy\mathrm{ }\,\,\mathrm{and }\,\,k > 0.

if the curve represented by

{\mathop\mathrm{Re}\nolimits} (u) + {\mathop\mathrm{Im}\nolimits} (u) = 1

intersects the Y-axis at the point

P\mathrm{ }\,\mathrm{and}\,\mathrm{ Q}

where

PQ=5

then the value of k is

View answer and explanation

Correct option: C

Option C (2) is correct because solving the equation derived from the given conditions yields k=2, considering k>0.