Complex Numbers: JEE Main Mathematics Previous Year Questions

417 previous year questions from Complex Numbers. Here are the 25 most important ones; open any question for the correct answer and a full step-by-step solution.

1. $The conjugate of a complex number is \frac{1}{i - 1} . Then, that complex number is$
2. $If α is a complex number such that α^{2} - α + 1 = 0, then α^{2011} =$
3. $Let z_{0} be a root of a quadratic equation, x^{2} + x + 1 = 0 . If z = 3 + 6 i z_{0}^{81} - 3 i z_{0}^{93}, then arg z is equal to:$
4. $Let z be the complex number satisfying | z - 5 | \leq 3 and having maximum positive principal argument. Then\dots$
5. $If x = - 5 + 2 - 4, then the value of the expression x^{4} + 9 x^{3} + 35 x^{2} - x + 4 is A .Find - A .$
6. $Let ω be the complex number cos \frac{2 π}{3} + i sin \frac{2 π}{3} . Then the number of distinct complex numbers z satisfying\dots$
7. $One of the 15^{th} roots of -1 is$
8. $Let z_{1} and z_{2} be two roots of the equation z^{2} + az + b = 0, z being complex. Further, assume that the origin, z_{1} and z_{2} for\dots$
9. $If z_{1} = 1 - 2 i; z_{2} = 1 + i and z_{3} = 3 + 4 i, then (\frac{1}{z _{1}} + \frac{3}{z _{2}}) \frac{z _{3}}{z _{2}} =$
10. $Let z be a complex number such that ∣ z ∣ + z = 3 + i (where i = - 1). Then ∣ z ∣ is equal to:$
11. $If z_{1} = 2 + 3 i, z_{2} = 4 - 5 i and z_{3} are are three points in the Argand plane such that\dots$
12. $If α, β and γ are the roots of the equation x^{3} - 8 x + 8 = 0, then \sum α^{2} and \sum \frac{1}{αβ} are respectively$
13. $\frac{( sin \frac{π}{8} + icos \frac{π}{8} ) ^{8}}{( sin \frac{π}{8} - icos \frac{π}{8} ) ^{8}} is equal\dots$
14. $If z - \frac{4}{z} = 2, then the maximum value of ∣ z ∣ is equal to:$
15. $The minimum value of | z - 1 | + | z - 5 | is$
16. $If ω is a complex cube root of unity, then sin ((ω^{10} + ω^{23}) π - \frac{π}{4}) =$
17. $For n \in N, let S_{n} = {z \in C : ∣ z - 3 + 2 i ∣ = \frac{n}{4}} and T_{n} = {z \in C : ∣ z - 2 + 3 i ∣ = \frac{1}{n}} . Then the number of elemen\dots$
18. $Sum of squares of modulus of all the complex numbers z satisfying z ˉ = i z^{2} + z^{2} - z is equal to$
19. $Let z \in C be such that ∣ z ∣ < 1 . If ω = \frac{5 + 3 z}{5 ( 1 - z )}, then:$
20. $If z_{1}, z_{2}, z_{3} are complex numbers such that ∣ z_{1} ∣ = ∣ z_{2} ∣ = ∣ z_{3} ∣ = \frac{1}{z _{1}} + \frac{1}{z _{2}} + \frac{1}{z _{3}} = 1 then ∣ z_{1} + z_{2} + z_{3} ∣ is$
21. $The area (in sq. units) of the triangle whose vertices are the points represented by the complex numbers 0, z, z e^{i α} (0 < α < π) is$
22. $If ω represents a complex cube root of unity, then\dots$
23. $ω is a complex cube root of unity. Match the items of List-I to the items of List-II.\dots$
24. $The locus of z = x + iy, such that Im (\frac{z - 3 i}{iz + 4}) = 0 is$
25. $If the roots of the equation (z - 4)^{3} = 8 i are a - 2 i, b + i and c + i, then abc is equal to$

Download Complex Numbers PYQs as PDF

Free questions PDF, 30 questions per set, with the Mere Teacher watermark and a QR code to the site. Answers and step-by-step solutions open after a free sign-up, with a download option too.

See all 417 Complex Numbers questions, free

Sign up free to practise them in your own custom test, with Concept Priority Question Bank, Test Series and BroBot AI help.

New here? See what Mere Teacher offers

Complex Numbers: JEE Main Mathematics Previous Year Questions

Download Complex Numbers PYQs as PDF

More JEE Main Mathematics chapters