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Complex Numbers question

2023 · 1 Feb · Shift 2 · Q33

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PYQ Library
JEE Main
Mathematics
Complex Numbers
2023 · 1 Feb · Shift 2 · Q33

Complex Numbers question

2023 · 1 Feb · Shift 2 · Q33

JEE MainMathematicsComplex NumbersMCQ+4 / −1

Let

a,b

be two real numbers such that

ab \lt 0

. IF the complex number

\frac{1+ai}{b+i}

is of unit modulus and

a+ib

lies on the circle

|z-1|=|2z|

, then a possible value of

\frac{1+[a]}{4b}

, where

[t]

is greatest integer function, is :

A
$\left(\frac{1+\sqrt{7}}{4}\right)$
B
$\frac{1}{2}$
C
0
D
$-$ 1

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