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Complex Numbers question

2017 · Shift 1 · Q21

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PYQ Library
JEE Advanced
Mathematics
Complex Numbers
2017 · Shift 1 · Q21

Complex Numbers question

2017 · Shift 1 · Q21

JEE AdvancedMathematicsComplex NumbersMultiple correct+4 / −1

Let a, b, x and y be real numbers such that a

-

b = 1 and y

e

0. If the complex number z = x + iy satisfies

{\mathop{\rm Im} olimits} \left( {{{az + b} \over {z + 1}}} \right) = y

, then which of the following is(are) possible value(s) of x?

A
$1 - \sqrt {1 + {y^2}}$
B
$- 1 - \sqrt {1 - {y^2}}$
C
$1 + \sqrt {1 + {y^2}}$
D
$- 1 + \sqrt {1 - {y^2}}$

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