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Complex Numbers question

2016 · Shift 2 · Q19

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PYQ Library
JEE Advanced
Mathematics
Complex Numbers
2016 · Shift 2 · Q19

Complex Numbers question

2016 · Shift 2 · Q19

JEE AdvancedMathematicsComplex NumbersMultiple correct+4 / −2

Let

a,\,b \in R\,and\,{a^{2\,}} + {b^2} e 0

. Suppose

S = \left\{ {Z \in C:Z = {1 \over {a + ibt}}, + \in R,t e 0} \right\}

, where

i = \sqrt { - 1}

. Ifz = x + iy and z

\in

S, then (x, y) lies on

A
the circle with radius ${{1 \over {2a}}}$ and centre $\left\{ {{1 \over {2a}},\,0} \right\}\,for\,a \gt 0\,,b e \,0$
B
the circle with radius $-{{1 \over {2a}}}$ and centre $\left\{ -{{1 \over {2a}},\,0} \right\}\,for\,a \lt 0\,,b e \,0$
C
the x-axis for $a e \,\,0,\,b e \,0$
D
the y-axis for $a = \,\,0,\,b e \,0$

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