Questions for JEE Main and Advanced for Complex Numbers. Some more algebra topics will be added soon.

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Complex Numbers
1: If then | eiz
| is equal to
a)
b)
c)
d)
2: The value of (where is
a) 0
b)
c)
d) i
3: If a complex number z lies on a circle of radius 1/2, then the complex number lies on a circle of
radius
a) 1/2
b) 1
c) 2
d) 4
4: If m and x are two real numbers, then (Where ) is equal to
a) cos x + i sin x
b) m/2
c) 1
d) (m + 1 )/2
5: If x = 2 + 5i (where ) and then the value of is
equal to
a) a

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b) b
c)
d)
6: The value of and are respectively (where )
a) 1296, 400
b) 72, 16
c) 36, 9
d) 216, 25
7: If z lies on the circle centred at origin. If area of the triangle whose vertices are z, and where is the
cube root of unity, is unit. Then radius of the circle is
a) 1 unit
b) 2 unit
c) 3 unit
d) 4 unit
8: If is a complex cube root of unity, then
a)
b) 0
c) 1
d)
9: The least positive integer n for which where x > 0 and is
a) 2
b) 4
c) 8
d) 12
10: Assertion : If | z1 | = 1, | z2 | = 2, | z3| = 3 and | z1 + 2z2 + 3z3 | = 6, then the value of | z2z3 + 8z3z1 + 27z1z2| is
36
Reason :

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a) Both assertion and reason are individually true and reason is the correct explanation of A
b) Both assertion and reason are individually true but reason is not the correct explanation of A
c) Assertion is true but reason is false
d) Assertion is false but reason is true
11: If z1 and z2 are any two complex numbers, then is equal to
a) | z1|
b) | z2|
c) | z1+ z2|
d) none of these
12: The centre of square ABCD is at z = 0. A is z1. Then the centroid of triangle ABC is
a)
b)
c)
d)
13: If where and n is an integer, then the total number of distinct values of S(n) is
a) 1
b) 2
c) 3
d) 4
14: If z1 and represent adjacent vertices of a regular polygon of n sides whose centre is origin and if
then n is equal to
a) 8
b) 16
c) 24
d) 32
15: If the points represent by complex numbers z1 = a + ib, z2 = c + id (where and are collinear,
then

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a) ad + bc = 0
b)
c) ab + cd = 0
d)
16: Let and be two distinct complex numbers such that If real part of is positive and imaginary
part of is negative, then the complex number may be
a) zero
b) real and negative
c) real and positive
d) purely imaginary
17: If be the n, nth roots of the unity, then the value of is equal to
a)
b)
c)
d)
18: For complex numbers z1 = x1 + iy1 and z2 = x2 + iy2, (where we write of and
then for all complex numbers z with we have is
a) 0
b) 1
c) 2
d) 3
19: The distance of the roots of the equation from z = 0 are
a) greater than 2/3
b) less than 2/3
c) greater than

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d) less than
20: Let (where and then is
a) 1
b)
c) i
d)