Exam (elaborations) jee mains 2024 pyq

Complex Number JEE Main 2024 January Question Bank

Questions with Answer Keys MathonGo

Q1 - 2024 (01 Feb Shift 1)

LetS = {z ∈ C : |z − 1| = 1 and (√2 − 1)(z + z̄ ) − i(z − z̄ ) = 2√2}. Let z 1, z2 ∈ S be such that
2
|z1 | = maxz∈s |z| and |z 2| = minz∈S |z| . Then ∣∣√2z 1 − z2 ∣
∣ equals :

(1) 1
(2) 4

(3) 3
(4) 2



Q2 - 2024 (01 Feb Shift 1)

Let P = {z ∈ C : |z + 2 − 3i| ≤ 1} and Q = {z ∈ C : z(1 + i) + z̄ (1 − i) ≤ −8}. Let in P ∩ Q, |z − 3 + 2i|

be maximum and minimum at z and z respectively. If |z , where α, β are integers,
2 2
1 2 1| + 2|z| = α + β √2


then α + β equals



Q3 - 2024 (01 Feb Shift 2)

If z is a complex number such that |z| ≥ 1, then the minimum value of ∣∣z + is:
1
(3 + 4i)∣
∣
2



[We changed options. In official NTA paper no option was correct.]

(1)
5

2



(2) 2
(3) 3
(4) 0



Q4 - 2024 (27 Jan Shift 1)

If S = {z ∈ C : |z − i| = |z + i| = |z − 1|} , then, n(S) is:

(1) 1

(2) 0
(3) 3
(4) 2

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, Complex Number JEE Main 2024 January Question Bank

Questions with Answer Keys MathonGo

Q5 - 2024 (27 Jan Shift 1)

If α satisfies the equation x 2
+ x + 1 = 0 and (1 + α) 7 2
= A + Bα + C , A, B, C ≥ 0 , then
5(3 A − 2 B − C) is equal to_____



Q6 - 2024 (27 Jan Shift 2)

Let the complex numbers α and 1

ᾱ
lie on the circles |z − z 0|
2
= 4 and |z − z 0|
2
= 16 respectively, where
z0 = 1 + i . Then, the value of 100|α| is. 2




Q7 - 2024 (29 Jan Shift 1)

If z = 1

2
− 2i , is such that |z + 1| = αz + β(1 + i), i = √−1 and α, β ∈ R , then α + β is equal to

(1) -4

(2) 3

(3) 2
(4) -1



Q8 - 2024 (29 Jan Shift 1)

Let α, β be the roots of the equation x 2
− x + 2 = 0 with Im(α) > Im(β). Then α 6
+ α
4
+ β
4
− 5α
2
is equal

to


Q9 - 2024 (29 Jan Shift 2)

Let r and θ respectively be the modulus and amplitude of the complex number z = 2 − i (2 tan 5π

8
) , then

(r, θ) is equal to

(1) (2 sec 3π

8
,
3π

8
)



(2) (2 sec 3π

8
,
5π

8
)



(3) (2 sec 5π

8
,
3π

8
)



(4) (2 sec 11π

8
,
11π

8
)




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