Let integers a, b \in[-3,3] be such that a+b \neq 0. Then the number of all possible ordered pairs (a, b), for which {| \frac{z-a}{z+b} |}=1 and \left|\begin{array}{ccc}z+1 & \omega & \omega^2 \ \omega & z+\omega^2 & 1 \ \omega^2 & 1 & z+\omega|\end{array}=1, z \in C, where \omega and \omega^2 are the roots of x^2+x+1=0, is equal to ______ . [29 Jan 2025 Shift 2]

Complex Numbers Part 2

Section: Mathematics

Question : 21 of 97

Marks: +1, -0

Let integers a,b∈[−3,3] be such that a+b≠0. Then the number of all possible ordered pairs (a,b), for which |‌

z−a

z+b

|=1 and
|

|=1,z∈C, where ω and ω2 are the roots of x2+x+1=0, is equal to ______ .

[29 Jan 2025 Shift 2]

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