Complex Numbers and Quadratic Equations

JEE Main 2025 (Online) 22nd January Morning ShiftMCQMedium📈 Topic in 5% papers+4−1

Ques. 1JEE Main 2025, 22 January (Morning Shift)

Let z1,z2 and z3 be three complex numbers on the circle |z|=1 with (z1)= - 4, (z2)=0 and (z3)= 4. If |z1 z2+z2 z3+z3 z1 |2= + 2, , Z, then the value of 2+ 2 is :

Answer

(2) 29

Solution

On |z|=1: z=ei , z=e-i , so products only add angles.

[figure]

z1 z2=e-i /4, z2 z3=e-i /4, z3 z1=ei /2=i

Sum = 2+i(1- 2)

|Sum|2=2+(1- 2)2=5-2 2 =5, =-2

2+ 2=29

Answer: (2)

Keep practising — Complex Numbers and Quadratic Equations

Ques. 2JEE Main 2025, 22 January (Evening Shift)

Let and be the distinct roots of 2x2+( )x-1=0, (0,2 ). If m and M are the minimum and the maximum values of 4+ 4, then 16(M+m) equals :

Ques. 3JEE Main 2025, 22 January (Evening Shift)

Let the curve z(1+i)+ z(1-i)=4, z , divide the region |z-3| 1 into two parts of areas and . Then | - | equals :

1+ 3
1+ 6
1+ 2
1+ 4

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