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MathsHardMCQ2023 · 01 Feb Shift 2

Q62.Let a, b be two real numbers such that ab < 0 . If the complex number 1+aib+i is of unit modulus and a + ib lies on the circle |z −1| = |2z| , then a possible value of 1+[a]4b , where [t] is greatest integer function, is : (1) 0 (2) −1 (3) 1 (4) 21

What This Question Tests

This multi-concept question combines conditions on the modulus of complex numbers and the geometric interpretation of a complex locus (circle) to find possible values involving the greatest integer function.

Concepts Tested

Modulus of a complex numberProperties of complex numbersGreatest integer function

Formulas Used

|z| = 1 => z * conjugate(z) = 1

|z₁/z₂| = |z₁|/|z₂|

|z − z₀| = k (circle equation)

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